## Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison

Gain some basic knowledge about the Fraction Equivalence and Comparison topics by accessing the free Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison. This resource of Go Math Grade 4 Answer Key aid your preparation for the standard tests. All the lessons covered in chapter 6 Fraction Equivalence and Comparison HMH Go Math Grade 4 Solution Key can be more efficient while your practice sessions. So, get the  Homework Help needed by referring to the Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison.

## Go Math Grade 4 Chapter 6 Fraction Equivalence and Comparison Answer Key

Download Go Math Grade 4 Solution Key Chapter 6 Fraction Equivalence and Comparison and prepare the concepts whenever you wish. Take the help from the given resource and solve the Grade 4 chapter 6 Fraction Equivalence and Comparison regularly to score high. Refer to the detailed Solutions presented here in Go Math Grade 4 Chapter 6 Fraction Equivalence and Comparison Answer Key and review your answers.

Lesson 1: Investigate • Equivalent Fractions

Lesson 2: Generate Equivalent Fractions

Lesson 3: Simplest Form

Lesson 4: Common Denominators

Lesson 5: Problem Solving • Find Equivalent Fractions

Mid-Chapter Checkpoint

Lesson 6: Compare Fractions Using Benchmarks

Lesson 7: Compare Fractions

Lesson 8: Compare and Order Fractions

Review/Test

### Common Core – Equivalent Fractions – Page No. 331

Equivalent Fractions
Use the model to write an equivalent fraction.

Question 1.

$$\frac{4}{6}=\frac{2}{3}$$

$$\frac{4}{6}=\frac{2}{3}$$

Explanation:
The first image has 4 parts shaded our of 6 parts. Divide $$\frac{8}{10}$$ with 2. You will get $$\frac{2}{3}$$. That means 2 parts are shaded out of 3 parts.

Question 2.

$$\frac{3}{4}$$ = $$\frac{□}{□}$$

$$\frac{3}{4}$$ = $$\frac{6}{8}$$

Explanation:
The first image has 3 parts shaded our of 4 parts. Multiply $$\frac{8}{10}$$ with 2. You will get $$\frac{6}{8}$$. That means 6 parts are shaded out of 8 parts.

Tell whether the fractions are equivalent. Write = or ≠.

Question 3.
$$\frac{8}{10}$$ _______ $$\frac{4}{5}$$

$$\frac{8}{10}$$ = $$\frac{4}{5}$$

Explanation:
Multiply the numerator and denominator of 4 / 5 with 2
8 / 10 = (2 / 2 ) x (4 / 5 )
= 8 / 10
So, 8 / 10 = 4 / 5.

Question 4.
$$\frac{1}{2}$$ _______ $$\frac{7}{12}$$

$$\frac{1}{2}$$ ≠ $$\frac{7}{12}$$

Explanation:
Multiply the numerator and denominator of 1 / 2 with 6
1 / 2 = (6 / 6) x (1 / 2)
= (6 / 12)
So, 1/2 ≠ 7 / 12

Question 8.
$$\frac{2}{6}$$ _______ $$\frac{4}{12}$$

$$\frac{2}{6}$$ = $$\frac{4}{12}$$

Explanation:
Multiply the numerator and denominator of 2 / 6 with 2
2 / 6 = (2 / 2) x (2 / 6)
= (4 / 12)
So, 2 / 6 = 4 / 12.

Question 9.
$$\frac{20}{100}$$ _______ $$\frac{1}{5}$$

$$\frac{20}{100}$$ = $$\frac{1}{5}$$

Explanation:
Cross Multiply the 20 / 100 with 20 / 20
20 / 100 = (20 / 20) x (20 / 100)
= (1 / 5)
So, 20 / 100 = 1 / 5.

Question 10.
$$\frac{5}{8}$$ _______ $$\frac{9}{10}$$

$$\frac{5}{8}$$ ≠ $$\frac{9}{10}$$

Explanation:
Multiply the numerator and denominator of 5 / 8 with 2
5 / 8 = (2 / 2) x (5 / 8)
= 10 / 16
So, 5 / 8 ≠ 9 / 10

Question 12.
Sophia’s vegetable garden is divided into 12 equal sections. She plants carrots in 8 of the sections. Write two fractions that are equivalent to the part of Sophia’s garden that is planted with carrots.
Type below:
___________

$$\frac{2}{3}$$ and $$\frac{4}{6}$$

Explanation:
As per the given data,
Sophia’s vegetable garden is divided into 12 equal sections
She plants carrots in 8 of the sections out of 12 sections = 8 / 12
By simplifying the 8 / 12, we will get 4 / 6
Again simplify the 4 /6 by dividing method, you will get 2 /3
2 / 3 = (2 / 2) x (2 / 3)
= 4 / 6
Then, the equivalent fractions are 2 / 3, 4 /6

### Common Core – Equivalent Fractions – Page No. 332

Question 1.
A rectangle is divided into 8 equal parts. Two parts are shaded. Which fraction is equivalent to the shaded area of the rectangle?
Options:
a. $$\frac{1}{4}$$
b. $$\frac{1}{3}$$
c. $$\frac{2}{6}$$
d. $$\frac{3}{4}$$

a. $$\frac{1}{4}$$

Explanation:
As per the given data,
A rectangle is divided into 8 equal parts
Then, the shaded area of rectangle = 2 / 8
By simplifying the 2/ 8, you will get 1/ 4
So, the shaded area of rectangle = 1 / 4

Question 2.
Jeff uses 3 fifth-size strips to model $$\frac{3}{5}$$. He wants to use tenth-size strips to model an equivalent fraction. How many tenth-size strips will he need?
Options:
a. 10
b. 6
c. 5
d. 3

b. 6

Explanation:
From the given data,
Jeff uses 3 fifth –size strips to model = 3 / 5 size strips
If he want to use tenth – size strips to an equivalent fraction = 1 / 10 size strips
The number of strips = x
(1 / 10) x = 3 / 5
x = 30/5
then, required number of tenth size trips = 6

Question 3.
Cassidy places 40 stamps on each of 8 album pages. How many stamps does she place in all?
Options:
a. 300
b. 320
c. 360
d. 380

b. 320

Explanation:
As per the given data,
Cassidy places 40 stamps on each of 8 album pages = 8 x 40
= 320
So, total placed stamps on album pages by Cassidy = 320 stamps

Question 4.
Maria and 3 friends have 1,200 soccer cards. If they share the soccer cards equally, how many will each person receive?
Options:
a. 30
b. 40
c. 300
d. 400

c. 300

Explanation:
As per the given data,
Maria and 3 friends have 1200 soccer cards
If soccer cards shared equally by four members = 1200/4
= 300
Then, each person received soccer cards = 300

Question 5.
Six groups of students sell 162 balloons at the school carnival. There are 3 students in each group. If each student sells the same number of balloons, how many balloons does each student sell?
Options:
a. 9
b. 18
c. 27
d. 54

a. 9

Explanation:
As per the given, data,
Six groups of students sell 162 balloons at the school carnival
There are 3 students in each group
Then, total number of students in 6 groups = 6 x 3 = 18
If each student sells the same number of balloons = 162 / 18
= 9
Number of balloons sells by each student = 9

Question 6.
Four students each made a list of prime numbers.
Eric: 5, 7, 17, 23
Maya: 3, 5, 13, 17
Bella: 2, 3, 17, 19
Jordan: 7, 11, 13, 21
Who made an error and included a composite number?
Options:
a. Eric
b. Maya
c. Bella
d. Jordan

d. Jordan

Explanation:
As per the given data,
Four students each made a list of prime numbers.
Eric: 5, 7, 17, 23
Maya: 3, 5, 13, 17
Bella: 2, 3, 17, 19
Jordan: 7, 11, 13, 21
21 is not a prime number
So, An error made by Jordan

### Page No. 335

Question 1.
Complete the table below.

Type below:
___________

Write two equivalent fractions.

Question 2.
$$\frac{4}{5}$$
$$\frac{4}{5}$$ = $$\frac { 4×□ }{ 5×□ }$$ = $$\frac{□}{□}$$
$$\frac{4}{5}$$ = $$\frac { 4×□ }{ 5×□ }$$ = $$\frac{□}{□}$$
$$\frac{4}{5}$$ = $$\frac{□}{□}$$ = $$\frac{□}{□}$$
Type below:
___________

$$\frac{4}{5}$$ = $$\frac{8}{10}$$ = $$\frac{80}{100}$$

Explanation:
Two equivalent fractions of 4/5,
(4/5) x (2/2) = 8/10
And
(4/5) x (20/20) = 80/100
8/10 = (8/10) (10/10)
= (80/100)
So, the equivalent fractions of 4/5 = 8/10, 80/100

Question 3.
$$\frac{2}{4}$$
$$\frac{2}{4}$$ = $$\frac { 2×□ }{ 4×□ }$$ = $$\frac{□}{□}$$
$$\frac{2}{4}$$ = $$\frac { 2×□ }{ 4×□ }$$ = $$\frac{□}{□}$$
$$\frac{2}{4}$$ = $$\frac{□}{□}$$ = $$\frac{□}{□}$$
Type below:
___________

$$\frac{2}{4}$$ = $$\frac{4}{8}$$ = $$\frac{8}{16}$$

Explanation:
Two equivalent fractions of 2/4,
(2/4) x (2/2) = 4/8
And
(2/4) x (4/4) = 8/16
4/8 = (4/8) (2/2)
= (8/16)
So, the equivalent fractions of 2/4 = 4/8, 8/16

Write two equivalent fractions.

Question 4.
$$\frac{3}{6}$$
$$\frac{3}{6}$$ = $$\frac{□}{□}$$ = $$\frac{□}{□}$$
Type below:
___________

$$\frac{3}{6}$$ = $$\frac{6}{12}$$ = $$\frac{12}{24}$$

Explanation:
Two equivalent fractions of 3/6,
(3/ 6) x (2/2) = 6/12
And
(3/6) x (4/ 4) = 12/24
6/12 = (6/12) (2/2)
= (12/24)
So, the equivalent fractions of 3/6 = 6/12, 12/24

Question 5.
$$\frac{3}{10}$$
$$\frac{3}{10}$$ = $$\frac{□}{□}$$ = $$\frac{□}{□}$$
Type below:
___________

$$\frac{3}{10}$$ = $$\frac{6}{20}$$ = $$\frac{12}{40}$$

Explanation:
Two equivalent fractions of 3/10,
(3/ 10) x (2/2) = 6/20
And
(3/10) x (4/ 4) = 12/40
6/20 = (6/20) (2/2)
= (12/40)
So, the equivalent fractions of 3/10 = 6/20, 12/40

Question 6.
$$\frac{2}{5}$$
$$\frac{2}{5}$$ = $$\frac{□}{□}$$ = $$\frac{□}{□}$$
Type below:
___________

$$\frac{2}{5}$$ = $$\frac{4}{10}$$ = $$\frac{8}{20}$$

Explanation:
Two equivalent fractions of 2/5,
(2/ 5) x (2/2) = 4/10
And
(2/5) x (4/ 4) = 8/20
4/10 = (4/10) (2/2)
= (8/20)
So, the equivalent fractions of 2/5 = 4/10, 8/20

Tell whether the fractions are equivalent. Write = or ≠.

Question 9.
$$\frac{1}{5}$$ ______ $$\frac{4}{10}$$

$$\frac{1}{5}$$ ≠ $$\frac{4}{10}$$

Explanation:
Multiply the numerator and denominator of 1/5 with 4
1/5 =(4/4) x (1/5)
= (4/20)
So, 1/5 ≠ 4/10

Question 10.
$$\frac{1}{4}$$ ______ $$\frac{2}{8}$$

$$\frac{1}{4}$$ = $$\frac{2}{8}$$

Explanation:
Multiply the numerator and denominator of 1/4 with 2
1/4 =(2/2) x (1/4)
= (2/8)
So, 1/4 = 2/8

### Page No. 336

Use the recipe for 11–12.

Question 11.
Kim says the amount of flour in the recipe can be expressed as a fraction. Is she correct? Explain.
______

As per the given data, Kim says the amount of flour in the recipe can be expressed as a fraction. But in the recipe, 1 tablespoon flour is added. So, Kim says wrong.

Question 12.
How could you use a $$\frac{1}{8}$$ – cup measuring cup to measure the light corn syrup?
Type below:
_________

As per the given data,
By using the 1/8 cup measure the 9/12 cup light corn syrup
(9/12)/(1/8) = (9 x 8)/12
= (3 x 8)/4
= (3 x 2)
= 6
So, required 6 cups of 1/8 to measure the light corn syrup of 9/12.

Question 13.
Communicate Explain using words how you know a fraction is equivalent to another fraction.
Type below:
_________

If you multiply the numerator and denominator of the first fraction by the same number and the products are the numerator and denominator of the second fraction, then the fractions are equivalent

### Common Core – Equivalent Fractions – Page No. 337

Write two equivalent fractions for each.

Question 1.

$$\frac{2}{6}$$ and $$\frac{4}{12}$$

Explanation:
1/3
(1/3) x (2/2) = 2/6
(1/3) x (4/4) = 4/12
So, the equivalent fractions of 1/3 are 2/6 and 4/12

Question 2.
$$\frac{2}{3}$$
Type below:
_________

$$\frac{4}{6}$$ and $$\frac{8}{12}$$

Explanation:
2/3
(2/3) x (2/2) = 4/6
(2/3) x (4/4) = 8/12
Then, the equivalent fractions of 2/3 = 4/6 and 8/12

Tell whether the fractions are equivalent. Write # or ≠.

Question 5.
$$\frac{1}{4}$$ ______ $$\frac{3}{12}$$

$$\frac{1}{4}$$ = $$\frac{3}{12}$$

Explanation:
1/4
Multiply the numerator and denominator of 1/4 with 3
Then, (1/4) x (3/3) = 3/12
So, 1/4 = 3/12

Question 6.
$$\frac{4}{5}$$ ______ $$\frac{5}{10}$$

$$\frac{4}{5}$$ ≠ $$\frac{5}{10}$$

Explanation:
4/5
Multiply numerator and denominator of 4/5 with 2
(4/5) x (2/2) = 8/10
Then 4/5 ≠ 5/10

Question 7.
$$\frac{3}{8}$$ ______ $$\frac{2}{6}$$

$$\frac{3}{8}$$ ≠ $$\frac{2}{6}$$

Explanation:
3/8 ≠ 2/6

Question 8.
$$\frac{3}{4}$$ ______ $$\frac{6}{8}$$

$$\frac{3}{4}$$ = $$\frac{6}{8}$$

Explanation:
3/4
Multiply the numerator and denominator of 3/4 with 2
Then, (3/4) x (2/2) = 6/8
So, 3/4 = 6/8

Question 9.
$$\frac{5}{6}$$ ______ $$\frac{10}{12}$$

$$\frac{5}{6}$$ = $$\frac{10}{12}$$

Explanation:
5/6
Multiply the numerator and denominator with 2
(5/6) x (2/2) = 10/12
So, 5/6 = 10/12

Question 10.
$$\frac{6}{12}$$ ______ $$\frac{5}{8}$$

$$\frac{6}{12}$$ ≠ $$\frac{5}{8}$$

Explanation:
6/12 ≠ 5/8

Question 11.
$$\frac{2}{5}$$ ______ $$\frac{4}{10}$$

$$\frac{2}{5}$$ = $$\frac{4}{10}$$

Explanation:
2/5
Multiply the numerator and denominator of 2/5 with 2
(2/5) x (2/2) = 4/10
So, 2/5 = 4/10

Question 12.
$$\frac{2}{4}$$ ______ $$\frac{3}{12}$$

$$\frac{2}{4}$$ ≠ $$\frac{3}{12}$$

Explanation:
2/4
Multiply the numerator and denominator of 2/4 with 3
(2/4) x (3/3) = 6/12
So, 2/4 ≠ 3/ 12

### Common Core – Equivalent Fractions – Page No. 338

Question 1.
Jessie colored a poster. She colored $$\frac{2}{5}$$ of the poster red. Which fraction is equivalent to $$\frac{2}{5}$$?
Options:
a. $$\frac{4}{10}$$
b. $$\frac{7}{10}$$
c. $$\frac{4}{5}$$
d. $$\frac{2}{2}$$

a. $$\frac{4}{10}$$

Explanation:
As per the given data,
Jessie colored a poster
She colored 2/5th of the poster red
Multiply the numerator and denominator of 2/5 with 2
Then, (2/5) x (2/2) = 4 /10
So, the equivalent fraction of 2/5 is 4/10

Question 2.
Marcus makes a punch that is $$\frac{1}{4}$$ cranberry juice. Which two fractions are equivalent to $$\frac{1}{4}$$?
Options:
a. $$\frac{2}{5}, \frac{3}{12}$$
b. $$\frac{2}{8}, \frac{4}{12}$$
c. $$\frac{3}{4}, \frac{6}{8}$$
d. $$\frac{2}{8}, \frac{3}{12}$$

d. $$\frac{2}{8}, \frac{3}{12}$$

Explanation:
As per the given data,
Marcus makes a punch that is 1/4th of cranberry juice
Multiply the numerator and denominator of 1/4 with 2
Then, (1/4) x (2/2) = 2/8
Multiply the numerator and denominator of 1/4 with 3
Then, (1/4) x (3/3) = 3/12
Equivalent fractions of 1/4 are 2/8 and 3/12

Question 3.
An electronics store sells a large flat-screen television for $1,699. Last month, the store sold 8 of these television sets. About how much money did the store make on the television sets? Options: a.$160,000
b. $16,000 c.$8,000
d. $1,600 Answer: b.$16,000

Explanation:
As per the given data,
An electronics store sells a large flat-screen television for $1,699 Last month, the store sold 8 of these television sets = 8 x$1,699 = $13,952. The money is about to$16,000.

Question 4.
Matthew has 18 sets of baseball cards. Each set has 12 cards. About how many baseball cards does Matthew have in all?
Options:
a. 300
b. 200
c. 150
d. 100

b. 200

Explanation:
From the given data,
Matthew has 18 sets of basketball cards
Each set has 12 cards = 12 x 18
= 216
Total number of basketball cards with Matthew = 216. So, it is near to 200.

Question 5.
Diana had 41 stickers. She put them in 7 equal groups. She put as many as possible in each group. She gave the leftover stickers to her sister. How many stickers did Diana give to her sister?
Options:
a. 3
b. 4
c. 5
d. 6

d. 6

Explanation:
As per the given data,
Diana has 41 stickers
She put them in 7 equal groups = 41/7
= 5 (remaining 6)
She gave the leftover stickers to her sister
The number of stickers Diana give to her sister = 6

Question 6.
Christopher wrote the number pattern below. The first term is 8.
8, 6, 9, 7, 10, …
Which is a rule for the pattern?
Options:

Explanation:
From the given data,
Christopher wrote the number pattern = 8, 6, 9, 7, 10, …..
The first number in the pattern = 8
8 – 2 = 6 + 3 = 9 – 2 = 7 +3 = 10 ….
So, the rule for the above pattern is to subtract 2, add 3

### Page No. 341

Question 1.
Write $$\frac{8}{10}$$ in simplest form.
$$\frac{8}{10}$$ = $$\frac { 8÷□ }{ 10÷□ }$$ = $$\frac{□}{□}$$
$$\frac{□}{□}$$

$$\frac{4}{5}$$

Explanation:
8/10 in simplest form
Divide the 8/10 with 2
(8/2)/(10/2) = 4/5
So, the simplest form of 8/10 is 4/5

Write the fraction in simplest form.

Question 2.
$$\frac{6}{12}$$
$$\frac{□}{□}$$

$$\frac{1}{2}$$

Explanation:
6/12 in simplest form
Divide the 6/12 with 6
(6/6)/(12/6) = 1/2
So, the simplest form of 6/12 is 1/2

Question 3.
$$\frac{2}{10}$$
$$\frac{□}{□}$$

$$\frac{1}{5}$$

Explanation:
2/10 in simplest form
Divide the 2/10 with 2
(2/2)/(10/2) = 1/5
So, the simplest form of 2/10 is 1/5

Question 4.
$$\frac{6}{8}$$
$$\frac{□}{□}$$

$$\frac{3}{4}$$

Explanation:
6/8 in simplest form
Divide the 6/8 with 2
(6/2)/(8/2) = 3/4
So, the simplest form of 6/8 is 3/4

Question 5.
$$\frac{4}{6}$$
$$\frac{□}{□}$$

$$\frac{2}{3}$$

Explanation:
4/6 in simplest form
Divide the 4/6 with 2
(4/2)/(6/2) = 2/3
So, the simplest form of 4/6 is 2/3

Write the fraction in simplest form.

Question 8.
$$\frac{10}{12}$$
$$\frac{□}{□}$$

$$\frac{5}{6}$$

Explanation:
10/12 in simplest form
Divide the 10/12 with 2
(10/2)/(12/2) = 5/6
So, the simplest form of 10/12 is 5/6

Question 9.
$$\frac{20}{100}$$
$$\frac{□}{□}$$

$$\frac{1}{5}$$

Explanation:
20 /100 in simplest form
Divide the 20/100 with 20
(20/20)/(100/20) = 1/5
So, the simplest form of 20/100 is 1/5

Tell whether the fraction is in simplest form. Write yes or no.

Question 10.
$$\frac{2}{8}$$
______

No

Explanation:
2/8 in simplest form
Divide the 2/8 with 2
(2/2)/(8/2) = 1/4
The simplest form of 2/8 is 1/4
So, 2/8 is not the simplest form

Question 11.
$$\frac{9}{12}$$
______

No

Explanation:
9/12 in simplest form
Divide the 9/12 with 3
(9/3)/(12/3) = 3/4
The simplest form of 9/12 is 3/4
So, 9/12 is not the simplest form

Question 12.
$$\frac{5}{6}$$
______

Yes

Explanation:
5/6 is not divided by any number
Yes, 5/6 is the simplest form

Question 13.
$$\frac{4}{10}$$
______

No

Explanation:
4/10 in simplest form
Divide the 4/10 with 2
(4/2)/(10/2) = 2/5
So, 4/10 is not the simplest form

Question 14.
There are 18 students in Jacob’s homeroom. Six students bring their lunch to school. The rest eat lunch in the cafeteria. In simplest form, what fraction of students eat lunch in the cafeteria?
$$\frac{□}{□}$$ of students

$$\frac{2}{3}$$ of students

Explanation:
As per the given data,
There are 18 students in Jacob’s homeroom
6 students bring their lunch to school = 6/18 = 1/3
The rest eat lunch in the cafeteria = 18 – 6 = 12/18
Divide the numerator and denominator of 12/18 with 6
(12/6) x (18/6) = 2/3
So, 2/3 of students eat lunch in the cafeteria

### Page No. 342

Use the map for 15−16.

Question 15.
Identify Relationships What fraction of the states in the southwest region share a border with Mexico? Is this fraction in simplest form?
$$\frac{□}{□}$$

Yes, $$\frac{3}{4}$$

Explanation:
As per the given data,
Southwest region states = 4
Number of states in the southwest region shares a border with Mexico out of total southwest region states = 3/4
Yes, 3/4 is the simplest form

Question 16.
What’s the Question? $$\frac{1}{3}$$ of the states in this region are on the Gulf of Mexico.
Type below:
_________

In the simplest form, what fraction of the states in the southeast area on the Gulf of Mexico.

Question 18.
In Michelle’s homeroom, $$\frac{9}{15}$$ of the students ride the bus to school, $$\frac{4}{12}$$ get a car ride, and $$\frac{2}{30}$$ walk to school.
For numbers 18a–18c, select True or False for each statement.
a. In simplest form, $$\frac{3}{5}$$ of the students ride the bus to school.
i. True
ii. False

i. True

Explanation:
9/15 of the students ride the bus to school
By dividing the numerator and denominator of 9/15 with 3
(9/3)/(15/3) =3/5
So, 3/5 of the students ride the bus to school
True

Question 18.
b. In simplest form, $$\frac{1}{4}$$ of the students get a car ride to school.
i. True
ii. False

ii. False

Explanation:
a. 4/12 of the students get a car ride
The simplest form of 4/12 = 1/3
So, 1/4 of the students get a car ride to school is a False statement

Question 18.
c. In simplest form, $$\frac{1}{15}$$ of the students walk to school.
i. True
ii. False

i. True

Explanation:
a. 2/30 of the students walk to school
By dividing the 2/30 with 2
(2/2)/(30/2) = 1/15
So, 1/15 of the students walk to school is a true statement

### Common Core – Simplest Form – Page No. 343

Write the fraction in simplest form.

Question 1.

$$\frac{3}{5}$$

Explanation:
To write the 6/10 in a simplest form
Divide the numerator and denominator of 6/10 with 2
(6 ÷2)/(10 ÷2) = 3/5
So, the simplest form of 6/10 = 3/5

Question 2.
$$\frac{6}{8}$$ = $$\frac{□}{□}$$

$$\frac{3}{4}$$

Explanation:
To write the 6/8in a simplest form
Divide the numerator and denominator of 6/8 with 2
(6 ÷2)/(8 ÷2) = 3/4
So, the simplest form of 6/8 = 3/4

Question 3.
$$\frac{5}{5}$$ = $$\frac{□}{□}$$

$$\frac{1}{1}$$ = 1

Explanation:
To write the 5/5in a simplest form
Divide the numerator and denominator of 5/5 with 5
(5 ÷5)/(5 ÷5) = 1/1
So, the simplest form of 5/5 = 1

Question 4.
$$\frac{8}{12}$$ = $$\frac{□}{□}$$

$$\frac{2}{3}$$

Explanation:
To write the 8/12in a simplest form
Divide the numerator and denominator of 8/12 with 4
(8 ÷4)/(12 ÷4) = 2/3
So, the simplest form of 8/12 = 2/3

Question 5.
$$\frac{100}{100}$$ = $$\frac{□}{□}$$

$$\frac{1}{1}$$ = 1

Explanation:
The simplest form of 100/100 = 1

Question 6.
$$\frac{2}{6}$$ = $$\frac{□}{□}$$

$$\frac{1}{3}$$

Explanation:
To write the 2/6in a simplest form
Divide the numerator and denominator of 2/6 with 2
(2 ÷2)/(6 ÷2) = 1/3
So, the simplest form of 2/6 = 1/3

Tell whether the fractions are equivalent. Write = or ≠. (if you dont have ≠on your keybord, copy and paste this one: ≠ )

Question 9.
$$\frac{6}{12}$$ _______ $$\frac{1}{12}$$

$$\frac{6}{12}$$ ≠ $$\frac{1}{12}$$

Explanation:
6/12 ≠ 1/12

Question 10.
$$\frac{3}{4}$$ _______ $$\frac{5}{6}$$

$$\frac{3}{4}$$ ≠ $$\frac{5}{6}$$

Explanation:
3/4 ≠ 5/6

Question 11.
$$\frac{6}{10}$$ _______ $$\frac{3}{5}$$

$$\frac{6}{10}$$ = $$\frac{3}{5}$$

Explanation:
6/10
Divide the numerator and denominator of 6/10 with 2
(6 ÷ 2)/( 10 ÷ 2) = 3/5
So, 6/10 = 3/5

Question 12.
$$\frac{3}{12}$$ _______ $$\frac{1}{3}$$

$$\frac{3}{12}$$ ≠ $$\frac{1}{3}$$

Explanation:
3/12 ≠ 1/3

Question 13.
$$\frac{6}{10}$$ _______ $$\frac{60}{100}$$

$$\frac{6}{10}$$ = $$\frac{60}{100}$$

Explanation:
6/10
Multiply the numerator and denominator of 6/10 with 10
(6 x 10)/(10 x 10) = 60/100
So, 6/10 = 60/100

Question 14.
$$\frac{11}{12}$$ _______ $$\frac{9}{10}$$

$$\frac{11}{12}$$ ≠ $$\frac{9}{10}$$

Explanation:
11/12 ≠ 9/10

Question 15.
$$\frac{2}{5}$$ _______ $$\frac{8}{20}$$

$$\frac{2}{5}$$ = $$\frac{8}{20}$$

Explanation:
2/5
Multiply the numerator and denominator of 2/5 with 4
(2 x 4)/(5 x 4) = 8/20
So, 2/5 = 8/20

Question 16.
$$\frac{4}{8}$$ _______ $$\frac{1}{2}$$

$$\frac{4}{8}$$ = $$\frac{1}{2}$$

Explanation:
4/8
Divide the numerator and denominator of 4/8 with 4
(4 x 4)/(8 x 4) = 1/2
So, 4/8 = 1/2

### Common Core – Simplest Form – Page No. 344

Question 1.
Six out of the 12 members of the school choir are boys. In the simplest form, what fraction of the choir are boys?
Options:
a. $$\frac{1}{6}$$
b. $$\frac{6}{12}$$
c. $$\frac{1}{2}$$
d. $$\frac{12}{6}$$

c. $$\frac{1}{2}$$

Explanation:
As per the given data,
Six out of the 12 members of the school choir are boys = 6/12
To write the simplest form of 6/12, divide the numerator and denominator with 6
Then, (6 ÷ 6)/(12 ÷ 6) = 1/2
In simplest form, 1/2 of the choir is boys

Question 2.
Which of the following fractions is in simplest form?
Options:
a. $$\frac{5}{6}$$
b. $$\frac{6}{8}$$
c. $$\frac{8}{10}$$
d. $$\frac{2}{12}$$

a. $$\frac{5}{6}$$

Explanation:
5/6 is in the simplest form
6/8 simplest form = 3/4
8/10 simplest form = 4/5
2/12 simplest form = 1/6

Question 3.
Each of the 23 students in Ms. Evans’ class raised $45 for the school by selling coupon books. How much money did the class raise in all? Options: a.$207
b. $225 c.$1,025
d. $1,035 Answer: d.$1,035

Explanation:
As per the given data,
Each of the 23 students in Ms. Evan’s class raised $45 for the school by selling coupon books = 23 x$45
= $1,035 Question 4. Which pair of numbers below have 4 and 6 as common factors? Options: a. 12, 18 b. 20, 24 c. 28, 30 d. 36, 48 Answer: d. 36, 48 Explanation: 36, 48 Here, 36 = 4 x 9 = 2 x 2 x 3 x 3 48 = 6 x 8 = 2 x 3 x 4 x 2 Question 5. Bart uses $$\frac{3}{12}$$ cup milk to make muffins. Which fraction is equivalent to $$\frac{3}{12}$$? Options: a. $$\frac{1}{4}$$ b. $$\frac{1}{3}$$ c. $$\frac{1}{2}$$ d. $$\frac{2}{3}$$ Answer: a. $$\frac{1}{4}$$ Explanation: As per the given data, Bart uses 3/12 cup milk to make muffins Divide the fraction with 3 (3 ÷ 3)/(12 ÷ 3) = 1/4 So, the equivalent fraction for 3/12 = 1/4 Question 6. Ashley bought 4 packages of juice boxes. There are 6 juice boxes in each package. She gave 2 juice boxes to each of 3 friends. How many juice boxes does Ashley have left? Options: a. 24 b. 22 c. 18 d. 12 Answer: c. 18 Explanation: As per the given data, Ashley bought 4 packages of juice boxes There are 6 juice boxes in each package = 6 x 4 = 24 She gave 2 juice boxes to each of 3 friends = 2 x 3 = 6 juice boxes So, 24 – 6 = 18 Total number of juice boxes left with Ashley = 18 ### Page No. 347 Question 1. Find a common denominator for $$\frac{1}{3}$$ and $$\frac{1}{12}$$ by dividing each whole into the same number of equal parts. Use the models to help. common denominator: Answer: common denominator: 12 Explanation: List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, …. List the multiples of 12 = 12, 24, 36, 48, …. So, common denominators of 1/3 and 1/ 12 is 12 Write the pair of fractions as a pair of fractions with a common denominator. Question 2. $$\frac{1}{2}$$ and $$\frac{1}{4}$$ Type below: _________ Answer: $$\frac{4}{8}$$ and $$\frac{2}{8}$$ Explanation: Common denominator of 1/2 and 1/4 List the multiples of 2 = 2, 4, 6, 8, 10, … List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . . Then, the common denominator of 1/2 and 1/4 is 4 For the Common pair of fractions, multiply the common denominator with fractions That is, (1 x 4) ÷( 2 x 4) and ( 1 x 4 ) ÷ ( 4 x 4) So, the common pair of fractions = 4/8 and 2/8 Question 3. $$\frac{3}{4}$$ and $$\frac{5}{8}$$ Type below: _________ Answer: $$\frac{6}{8}$$ and $$\frac{5}{8}$$ Explanation: Common denominator of 3/4 and 5/8 List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . . List the multiples of 8 = 8, 16, 24, 32, . . . . Then, the common denominator of 3/4 and 5/8 is 8 For the Common pair of fractions, multiply the common denominator with fractions That is, (3 x 8) ÷( 4 x 8) and ( 5 x 8 ) ÷ ( 8 x 8) So, the common pair of fractions = 6/8 and 5/8 Question 4. $$\frac{1}{3}$$ and $$\frac{1}{4}$$ Type below: _________ Answer: $$\frac{4}{12}$$ and $$\frac{3}{12}$$ Explanation: The common denominator of 1/3 and 1/4 List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, …. List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . . Then, the common denominator of 1 /3 and 1/4 is 12 For the Common pair of fractions, multiply the common denominator with fractions That is, (1 x 12) ÷( 3 x 12) and ( 1 x 12 ) ÷ ( 4 x 12) So, the common pair of fractions = 4/12 and 3/12 Question 5. $$\frac{4}{12}$$ and $$\frac{5}{8}$$ Type below: _________ Answer: $$\frac{8}{24}$$ and $$\frac{15}{24}$$ Explanation: Common denominator of 4/12 and 5/8 List the multiples of 12 = 12, 24, 36, 48, 60, ….. List the multiples of 8 = 8, 16, 24, 32, 40, 48, … Then, the common denominator of 4/12 and 5/8 is 24 For the Common pair of fractions, multiply the common denominator with fractions That is, (4 x 24) ÷( 12 x 24) and ( 5 x 24 ) ÷ ( 8 x 24) So, the common pair of fractions = 8/24 and 15/24 Write the pair of fractions as a pair of fractions with a common denominator. Tell whether the fractions are equivalent. Write = or ≠. Question 8. $$\frac{3}{4}$$ ______ $$\frac{1}{2}$$ Answer: $$\frac{3}{4}$$ ≠ $$\frac{1}{2}$$ Explanation: 3/4 ≠ 1/2 Question 9. $$\frac{3}{4}$$ ______ $$\frac{6}{8}$$ Answer: $$\frac{3}{4}$$ = $$\frac{6}{8}$$ Explanation: 3/4 Multiply the numerator and denominator of 3/4 with 2 (3 x 2) ÷ ( 4 x 2 ) = 6/8 So, 3/4 = 6/8 Question 10. $$\frac{1}{2}$$ ______ $$\frac{4}{8}$$ Answer: $$\frac{1}{2}$$ = $$\frac{4}{8}$$ Explanation: 1/2 Multiply the numerator and denominator of 1/2 with 4 (1 x 4) ÷ ( 2 x 4 ) = 4/8 So, 1/2 = 4/8 Question 11. $$\frac{6}{8}$$ ______ $$\frac{4}{8}$$ Answer: $$\frac{6}{8}$$ ≠ $$\frac{4}{8}$$ Explanation: 6/8 ≠ 4/8 Question 12. Jerry has two same-size circles divided into the same number of equal parts. One circle has $$\frac{3}{4}$$ of the parts shaded, and the other has $$\frac{2}{3}$$ of the parts shaded. His sister says the least number of pieces each circle could be divided into is 7. Is his sister correct? Explain. ______ Answer: As per the given data, Jerry has two same size circles divided into the same number of equal parts One circle has 3/4 of the parts shaded So, non- shaded parts of one circle = 1 – 3/4 = 1/4 Another circle has 2/3 of the parts shaded Non – shaded parts = 1 – 2/3 = 1/3 We can’t draw a conclusion that in how many parts or pieces a circle can be divided So, his sister is incorrect ### Page No. 348 Question 13. Carrie has a red streamer that is $$\frac{3}{4}$$ yard long and a blue streamer that is $$\frac{5}{6}$$ yard long. She says the streamers are the same length. Does this make sense? Explain. ______ Answer: Carrie has a red streamer that is 3/4 yard long The blue streamer is 5/6 yard long 3/4 ≠ 5/6 She says the streamers are the same length, it doesn’t make any sense. Question 14. Leah has two same-size rectangles divided into the same number of equal parts. One rectangle has $$\frac{1}{3}$$ of the parts shaded, and the other has $$\frac{2}{5}$$ of the parts shaded. What is the least number of parts into which both rectangles could be divided? ______ parts Answer: 15 parts Explanation: As per the given data, Leah has two same size rectangles divided into the same number of equal parts One rectangle has 1/3 of the parts shaded Another rectangle has 2/5 of the parts shaded 15 parts Question 15. Julian says a common denominator for $$\frac{3}{4}$$ and $$\frac{2}{5}$$ is 9. What is Julian’s error? Explain. Type below: ___________ Answer: As per the given data, Julian says a common denominator for 3/4 and 2/5 is 9 To find the common denominator for 3/4 and 2/5 List the multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, ….. List the multiples of 5 = 5, 10, 15, 20, 25, 30, …. So, the common denominator for 3/4 and 2/5 is 20 Julian says 9 in place of 20 and it is wrong. Question 16. Miguel has two same-size rectangles divided into the same number of equal parts. One rectangle has $$\frac{3}{4}$$ of the parts shaded, and the other has $$\frac{5}{8}$$ of the parts shaded. Into how many parts could each rectangle be divided? Show your work by sketching the rectangles. ______ parts Answer: 8 parts Explanation: As per the given data, Miguel has two same – size rectangles divided into the same number of equal parts. One rectangle has 3/4 of the parts shaded. Another has 5/8 of the parts shaded. The possible parts are 8. ### Common Core – Common Denominators – Page No. 349 Write the pair of fractions as a pair of fractions with a common denominator. Question 1. $$\frac{2}{3} \text { and } \frac{3}{4}$$ Answer: $$\frac{8}{12} \text { and } \frac{9}{12}$$ Explanation: 2/3 and 3/4 List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, … List the multiples of 4 = 4, 8, 12, 16, 20, … Common multiple of 3 and 4 is 12 For the Common pair of fractions, multiply the common denominator with fractions That is, (2 x 12) ÷( 3 x 12) and ( 3 x 12 ) ÷ ( 4 x 12) So, common pair of fractions = 8/12 and 9/12 Question 2. $$\frac{1}{4} \text { and } \frac{2}{3}$$ Type below: _________ Answer: $$\frac{3}{12} \text { and } \frac{8}{12}$$ Explanation: 1/4 and 2/3 List the multiples of 4 = 4, 8, 12, 16, 20, … List the multiples of 3 = 3, 6, 9, 12, 15, 18, … Common multiple of 4 and 3 is 12 For the Common pair of fractions, multiply the common denominator with fractions That is, (1 x 12) ÷( 4 x 12) and ( 2 x 12 ) ÷ ( 3 x 12) So, common pair of fractions = 3/12 and 8/12 Question 3. $$\frac{3}{10} \text { and } \frac{1}{2}$$ Type below: _________ Answer: $$\frac{3}{10} \text { and } \frac{5}{10}$$ Explanation: 3/10 and 1/2 List the multiples of 10 = 10, 20, 30, 40, 50, …. List the multiples of 2 = 2, 4, 6, 8, 10, 12, 14, …. Common multiple of 10 and 2 is 10 For the Common pair of fractions, multiply the common denominator with fractions That is, (3 x 10) ÷( 10 x 10) and ( 1 x 10 ) ÷ ( 2 x 10) So, common pair of fractions = 3/10 and 5/10 Question 4. $$\frac{3}{5} \text { and } \frac{3}{4}$$ Type below: _________ Answer: $$\frac{12}{20} \text { and } \frac{15}{20}$$ Explanation: 3/5 and 3/4 List the multiples of 5 = 5, 10, 15, 20, 25, 30, …. List the multiples of 4 = 4, 8, 12, 16, 20, 24, … Common multiple of 5 and 4 is 20 For the Common pair of fractions, multiply the common denominator with fractions That is, (3 x 20) ÷( 5 x 20) and ( 3 x 20 ) ÷ ( 4 x 20) So, common pair of fractions = 12/20 and 15/20 Question 7. $$\frac{1}{4} \text { and } \frac{1}{6}$$ Type below: _________ Answer: $$\frac{3}{12} \text { and } \frac{2}{12}$$ Explanation: 1/4 and 1/6 List the multiples of 4 = 4, 8, 12, 16, 20, 24, … List the multiples of 6 = 6, 12, 18, 24, 30, … Common multiple of 4 and 6 is 12 For the Common pair of fractions, multiply the common denominator with fractions That is, (1 x 12) ÷( 4 x 12) and ( 1 x 12 ) ÷ ( 6 x 12) So, common pair of fractions = 3/12 and 2/12 Tell whether the fractions are equivalent. Write = or ≠. Question 8. $$\frac{1}{2}$$ ______ $$\frac{2}{5}$$ Answer: $$\frac{1}{2}$$ ≠ $$\frac{2}{5}$$ Explanation: Multiply the numerator and denominator of 1/2 with 2 (1 x 2) ÷ (2 x 2) = 2/4 So, 1/2 ≠ 2/5 Question 9. $$\frac{1}{2}$$ ______ $$\frac{3}{6}$$ Answer: $$\frac{1}{2}$$ = $$\frac{3}{6}$$ Explanation: 1/2 Multiply the numerator and denominator of 1/2 with 3 (1 x 3) ÷ (2 x 3) = 3/6 So, 1/2 = 3/6 Question 10. $$\frac{3}{4}$$ ______ $$\frac{5}{6}$$ Answer: $$\frac{3}{4}$$ ≠ $$\frac{5}{6}$$ Explanation: 3/4 ≠ 5/6 Question 11. $$\frac{6}{10}$$ ______ $$\frac{3}{5}$$ Answer: $$\frac{6}{10}$$ = $$\frac{3}{5}$$ Explanation: 6/10 Divide the numerator and denominator of 6/10 with 2 (6 ÷ 2)/(10 ÷2) = 3/5 So, 6/10 = 3/5 Question 12. $$\frac{6}{8}$$ ______ $$\frac{3}{4}$$ Answer: $$\frac{6}{8}$$ = $$\frac{3}{4}$$ Explanation: 6/8 Divide the numerator and denominator of 6/8 with 2 (6 ÷2)/(8 ÷2) = 3/4 So, 6/8 = 3/4 Question 13. $$\frac{3}{4}$$ ______ $$\frac{2}{3}$$ Answer: $$\frac{3}{4}$$ ≠ $$\frac{2}{3}$$ Explanation: 3/4 ≠ 2/3 Question 14. $$\frac{2}{10}$$ ______ $$\frac{4}{5}$$ Answer: $$\frac{2}{10}$$ ≠ $$\frac{4}{5}$$ Explanation: 2/10 Divide the numerator and denominator of 2/10 with 2 (2 ÷ 2)/(10 ÷ 2) = 1/5 So, 2/10 ≠ 1/5 Question 15. $$\frac{1}{4}$$ ______ $$\frac{3}{12}$$ Answer: $$\frac{1}{4}$$ = $$\frac{3}{12}$$ Explanation: 1/4 Multiply the numerator and denominator of 1/4 with 3 (1 x 3)/(4 x 3) = 3/12 So, 1/4 = 3/12 Question 16. Adam drew two same size rectangles and divided them into the same number of equal parts. He shaded $$\frac{1}{3}$$ of one rectangle and $$\frac{1}{4}$$ of other rectangle. What is the least number of parts into which both rectangles could be divided? _________ Answer: 12 parts Explanation: As per the given data, Adam drew two same size rectangles and divided them into the same number of equal parts He shaded 1/3 of one rectangle 1/4 of another rectangle List the multiples of 3 = 3, 6, 9, 12, 15, 18, … List the multiples of 4 = 4, 8, 12, 16, 20, … A common multiple of 3 and 4 is 12 So, the least number of parts which rectangles could be divided = 12 parts Question 17. Mera painted equal sections of her bedroom wall to make a pattern. She painted $$\frac{2}{5}$$ of the wall white and $$\frac{1}{2}$$ of the wall lavender. Write an equivalent fraction for each using a common denominator. Type below: _________ Answer: 1/2 are 4/10 and 5/10 Explanation: As per the given data, Mera painted equal sections of her bedroom wall to make a pattern She painted 2/5 of the wall white and 1/2 of the wall lavender List the multiples of 5 = 5, 10, 15, 20, 25, 30, … List the multiples of 2 = 2 ,4, 6, 8, 10, 12, 14, … The common denominator of 2/5 and 1/2 = 10 Multiply the 2/5 and 1/2 with 10 (2 x 10)/(5 x 10) and (1 x 10)/(2 x 10) 4/10 and 5/10 So, common fractions of 2/5 and 1/2 are 4/10 and 5/10 ### Common Core – Common Denominators – Page No. 350 Question 1. Which of the following is a common denominator of $$\frac{1}{4}$$ and $$\frac{5}{6}$$? Options: a. 8 b. 9 c. 12 d. 15 Answer: c. 12 Explanation: Common denominator of 1/4 and 5/6 List the multiples of 4 = 4, 8, 12, 16, 20, 24, … List the multiples of 6 = 6, 12, 18, 24, 30, …. So, the common denominator of 1/4 and 5/6 is 12 Question 2. Two fractions have a common denominator of 8. Which of the following could be the two fractions? Options: a. $$\frac{1}{2} \text { and } \frac{2}{3}$$ b. $$\frac{1}{4} \text { and } \frac{1}{2}$$ c. $$\frac{3}{4} \text { and } \frac{1}{6}$$ d. $$\frac{1}{2} \text { and } \frac{4}{5}$$ Answer: b. $$\frac{1}{4} \text { and } \frac{1}{2}$$ Explanation: As per the given data, Two fractions have a common denominator of 8 a. 1/2 and 2/3 List the multiples of 2 = 2, 4, 6, 8,10, …. List the multiples of 3 = 3, 6, 9, 12, … There is no common denominator of 8 for 1/2 and 2/3 b. 1/4 and 1 /2 List the multiples of 2 = 2, 4, 6, 8,10, …. List the multiples of 4 = 4, 8, 12, 16, … Here, the common denominator of 1 /4 and 1 /2 is 8 So, the answer is 1/4 and 1/2 Question 3. Which number is 100,000 more than seven hundred two thousand, eighty-three? Options: a. 703,083 b. 712,083 c. 730,083 d. 802,083 Answer: d. 802,083 Explanation: 802,083 Question 4. Aiden baked 8 dozen muffins. How many total muffins did he bake? Options: a. 64 b. 80 c. 96 d. 104 Answer: c. 96 Explanation: As per the given data, Aiden baked 8 dozen muffins 1 dozen = 12 then, 8 dozens = 12 x 8 = 96 So, Aiden baked totally 96 muffins Question 5. On a bulletin board, the principal, Ms. Gomez, put 115 photos of the fourthgrade students in her school. She put the photos in 5 equal rows. How many photos did she put in each row? Options: a. 21 b. 23 c. 25 d. 32 Answer: b. 23 Explanation: As per the given data, On a bulletin board, the principal, Ms. Gomez, put 115 photos of the fourth-grade students in her school She put the photos in 5 equal rows Then, number of photos in each row = 115/5 = 23 So, Ms. Gomez put photos in each row = 23 Question 6. Judy uses 12 tiles to make a mosaic. Eight of the tiles are blue. What fraction, in simplest form, represents the tiles that are blue? Options: a. $$\frac{2}{3}$$ b. $$\frac{2}{5}$$ c. $$\frac{3}{4}$$ d. $$\frac{12}{18}$$ Answer: a. $$\frac{2}{3}$$ Explanation: As per the given data, Judy uses 12 tiles to make a mosaic Eight of the tiles are blue = 8/12 Divide the numerator and denominator of 8/12 with 4 (8 ÷ 4)/(12 ÷ 4) = 2/3 The simplest form of 8/12 is 2/3 ### Page No. 353 Question 1. Keisha is helping plan a race route for a 10-kilometer charity run. The committee wants to set up the following things along the course. Viewing areas: At the end of each half of the course Water stations: At the end of each fifth of the course Distance markers: At the end of each tenth of the course Which locations have more than one thing located there? First, make a table to organize the information. Next, identify a relationship. Use a common denominator, and find equivalent fractions. Finally, identify the locations at which more than one thing will be set up. Circle the locations. Type below: ___________ Answer: Keisha is helping plan a race route for a 10-kilometer charity run. Question 2. What if distance markers will also be placed at the end of every fourth of the course? Will any of those markers be set up at the same location as another distance marker, a water station, or a viewing area? Explain. Type below: ___________ Answer: It really depends on where you place the other markers. Question 3. Fifty-six students signed up to volunteer for the race. There were 4 equal groups of students, and each group had a different task. How many students were in each group? _____ students Answer: 14 students Explanation: As per the given data, Fifty-six students signed up to volunteer for the race There are four groups of students Number of students in each group = 56/4 = 14 Total number of students in each group = 14 ### Page No. 354 Question 6. Luke threw balls into these buckets at a carnival. The number on the bucket gives the number of points for each throw. What is the least number of throws needed to score exactly 100 points? Explain. _____ throws Answer: 13 throws Explanation: Take the maximum number to get the minimum throws = 9 X 10 = 90. 6 X 1 = 6; 2 X 2 = 4. Add 90 + 6 + 4 = 100; So, the least number of throws needed to score exactly 100 points = 10 + 1 + 2 = 13. Question 7. Victoria arranges flowers in vases at her restaurant. In each arrangement, $$\frac{2}{3}$$ of the flowers are yellow. What other fractions can represent the part of the flowers that are yellow? Shade the models to show your work. $$\frac{□}{□}$$ Answer: $$\frac{2}{3}$$, $$\frac{8}{12}$$, $$\frac{40}{60}$$ Explanation: Basically, any fraction obtained by multiplying both the numerator and denominator by the same value would be an equivalent fraction: 2/3 = 2/3 * 4/4 = 8/12 8/12 = 8/12 * 5/5 = 40/60 etc. ### Common Core – Find Equivalent Fractions – Page No. 355 Question 1. Miranda is braiding her hair. Then she will attach beads to the braid. She wants $$\frac{1}{3}$$ of the beads to be red. If the greatest number of beads that will fit on the braid is 12, what other fractions could represent the part of the beads that are red? Answer: $$\frac{2}{6}$$, $$\frac{3}{9}$$, $$\frac{4}{12}$$ Explanation: Miranda is braiding her hair. Then she will attach beads to the braid. She wants $$\frac{1}{3}$$ of the beads to be red. If the greatest number of beads that will fit on the braid is 12. $$\frac{1}{3}$$ X $$\frac{2}{2}$$ = $$\frac{2}{6}$$ $$\frac{1}{3}$$ X $$\frac{3}{3}$$ = $$\frac{3}{9}$$ $$\frac{1}{3}$$ X $$\frac{4}{4}$$ = $$\frac{4}{12}$$ Question 2. Ms. Groves has trays of paints for students in her art class. Each tray has 5 colors. One of the colors is purple. What fraction of the colors in 20 trays is purple? $$\frac{□}{□}$$ Answer: $$\frac{20}{100}$$ or $$\frac{1}{5}$$ Explanation: If you have 20 trays that are 100 colors with 20 being purple. 20/ 100 is 1/5 Question 3. Miguel is making an obstacle course for field day. At the end of every sixth of the course, there is a tire. At the end of every third of the course, there is a cone. At the end of every half of the course, there is a hurdle. At which locations of the course will people need to go through more than one obstacle? Type below: _________ Answer: $$\frac{1}{3}$$, $$\frac{1}{2}$$, $$\frac{2}{3}$$ and final locations Explanation: We have three fractions with different denominators: sixths, thirds, and halves. The first step is to make all the denominators equal for 1/6, 1/3, 1/2. In this case, we want sixths since LCM(2, 3, 6) = 6 since 1/3 = 2/6, and 1/2 = 3/6. Now we can start solving. 1. There are six tires at the following: 1/6, 2/6, 3/6, 4/6, 5/6, and 6/6. 2. There are three cones at the following (G.C.F.): 2/6 (or 1/3), 4/6 (or 2/3), and 6/6 (or 3/3). 3. There are two hurdles at the following (G.C.F.): 3/6 (or 1/2) and 6/6 (or 2/2). We look for common numbers. 1. On 2/6, there are two obstacles: a tire and a cone. 2. On 3/6, there are two obstacles: a tire and a hurdle. 3. On 4/6, there are two obstacles: a tire and a cone. 4. At 6/6, there are three obstacles: a tire, cone, and a hurdle. 2/6 = 1/3 3/6 = 1/2 4/6 = 2/3 6/6 = 1 The answers are 1/3, 1/2, 2/3, and 1. Question 4. Preston works in a bakery where he puts muffins in boxes. He makes the following table to remind himself how many blueberry muffins should go in each box. How many blueberry muffins should Preston put in a box with 36 muffins? _________ Answer: 12 blueberry muffins Explanation: Preston works in a bakery where he puts muffins in boxes. He makes the following table to remind himself how many blueberry muffins should go in each box. So, he had 2 blueberry muffins out of 6 muffins. 2/6 X 2/2 = 4/12. 4 blueberry muffins out of 12 muffins. 2/6 X 4/4 = 8/24. 8 blueberry muffins out of 24 muffins. 2/6 X 6/6 = 12/36. 12 blueberry muffins out of 36 muffins. ### Common Core – Find Equivalent Fractions – Page No. 356 Question 1. A used bookstore will trade 2 of its books for 3 of yours. If Val brings in 18 books to trade, how many books can she get from the store? Options: a. 9 b. 12 c. 18 d. 27 Answer: b. 12 Explanation: A used bookstore will trade 2 of its books for 3 of yours. If Val brings in 18 books to trade 2/3 X 6/6 = 12/18, she get 12 books Question 2. Every $$\frac{1}{2}$$ hour Naomi stretches her neck; every $$\frac{1}{3}$$ hour she stretches her legs; and every $$\frac{1}{6}$$ hour she stretches her arms. Which parts of her body will Naomi stretch when $$\frac{2}{3}$$ of an hour has passed? Options: a. neck and legs b. neck and arms c. legs and arms d. none Answer: c. legs and arms Explanation: Summing $$\frac{1}{2}$$‘s only gives integer values giving 1, 2, 3, 4…or integer values +$$\frac{1}{2}$$ and 0 + $$\frac{1}{2}$$ = $$\frac{1}{2}$$, 1 $$\frac{1}{2}$$, 2 $$\frac{1}{2}$$… So neck is excluded Every $$\frac{1}{3}$$: $$\frac{1}{3}$$ + $$\frac{1}{2}$$ = $$\frac{2}{3}$$ Legs will be stretched at $$\frac{2}{3}$$ hour Every $$\frac{1}{6}$$: $$\frac{1}{6}$$ + $$\frac{1}{6}$$ + $$\frac{1}{6}$$ + $$\frac{1}{6}$$ = $$\frac{4}{6}$$ Divide top and bottom by 2 giving: (4 ÷ 2)/(6 ÷ 2) = $$\frac{2}{3}$$ Arms will be stretched at latex]\frac{2}{3}[/latex] hour Question 3. At the beginning of the year, the Wong family car had been driven 14,539 miles. At the end of the year, their car had been driven 21,844 miles. How many miles did the Wong family drive their car during that year? Options: a. 6,315 miles b. 7,295 miles c. 7,305 miles d. 36,383 miles Answer: c. 7,305 miles Explanation: If at the beginning of the year, the Wong family’s car had driven 14539 miles and at the end of the year, it had driven 21844 miles, then subtract 14539 from 21844 to determine the difference between the two values, which will tell you how many miles the Wong family drove their car for during the year. 21844 – 14539 = 7305 miles Question 4. Widget Company made 3,600 widgets in 4 hours. They made the same number of widgets each hour. How many widgets did the company make in one hour? Options: a. 80 b. 90 c. 800 d. 900 Answer: d. 900 Explanation: 3,600 widgets in 4 hours therefore 3,600 / 4 for one hour = 900 widgets 900 widgets in one hour. Question 5. Tyler is thinking of a number that is divisible by 2 and by 3. By which of the following numbers must Tyler’s number also be divisible? Options: a. 6 b. 8 c. 9 d. 12 Answer: a. 6 Explanation: The number 6 is divisible by 2 and by 3. Question 6. Jessica drew a circle divided into 8 equal parts. She shaded 6 of the parts. Which fraction is equivalent to the part of the circle that is shaded? Options: a. $$\frac{2}{3}$$ b. $$\frac{3}{4}$$ c. $$\frac{10}{16}$$ d. $$\frac{12}{18}$$ Answer: b. $$\frac{3}{4}$$ Explanation: Jessica drew a circle divided into 8 equal parts. She shaded 6 of the parts. 6/8 = 3/4 ### Page No. 357 Choose the best term from the box. Question 1. ________ name the same amount. ________ Answer: Equivalent Fractions Question 2. A _________ is a common multiple of two or more denominators ________ Answer: Common Denominator Write two equivalent fractions. Question 5. $$\frac{3}{4}$$ Type below: ________ Answer: $$\frac{6}{8}$$ and $$\frac{9}{12}$$ Explanation: Two equivalent fractions of 3/4 Multiply the 3/4 with 2 (3 x 2)/(4 x 2) = 6/8 Multiply the 3/4 with 3 (3 x 3)/(4 x 3) = 9/12 So, the equivalent fractions of 3/4 are 6/8 and 9/12 Tell whether the fractions are equivalent. Write = or ≠. Question 6. $$\frac{2}{3}$$ ______ $$\frac{4}{12}$$ Answer: $$\frac{2}{3}$$ ≠ $$\frac{4}{12}$$ Explanation: 2/ 3 Multiply the numerator and denominator of 2/3 with 2 (2 x 2)/(3 x 2) = 4/6 So, 2/3 ≠ 4/12 Question 7. $$\frac{5}{6}$$ ______ $$\frac{10}{12}$$ Answer: $$\frac{5}{6}$$ =_ $$\frac{10}{12}$$ Explanation: 5/6 Multiply the 5/6 with 2 (5 x 2)/(6 x 2) = 10/12 So, 5/6 = 10/12 Question 8. $$\frac{1}{4}$$ ______ $$\frac{4}{8}$$ Answer: $$\frac{1}{4}$$ ≠ $$\frac{4}{8}$$ Explanation: 1/4 Multiply the numerator and denominator of 1/4 with 4 (1 x 4)/(4 x 4) = 4/16 So, 1/4 ≠ 4/8 Write the fraction in simplest form. Question 9. $$\frac{6}{8}$$ $$\frac{□}{□}$$ Answer: $$\frac{3}{4}$$ Explanation: 6/8 Divide the numerator and denominator of 6/8 with 2 (6 ÷ 2)/( 8 ÷ 2) = 3/4 The simplest form of 6/8 is 3/4 Question 10. $$\frac{25}{100}$$ $$\frac{□}{□}$$ Answer: $$\frac{1}{4}$$ Explanation: 25/100 Divide the numerator and denominator of 25/100 with 25 (25 ÷ 25)/( 100 ÷ 25) = 1/4 The simplest form of 25/100 is 1/4 Question 11. $$\frac{8}{10}$$ $$\frac{□}{□}$$ Answer: $$\frac{4}{5}$$ Explanation: 8/10 Divide the numerator and denominator of 8/10 with 2 (8 ÷ 2)/( 10 ÷ 2) = 4/5 The simplest form of 8/10 is 4/5 Write the pair of fractions as a pair of fractions with a common denominator. ### Page No. 358 Question 14. Sam needs $$\frac{5}{6}$$ cup mashed bananas and $$\frac{3}{4}$$ cup mashed strawberries for a recipe. He wants to find whether he needs more bananas or more strawberries. How can he write $$\frac{5}{6}$$ and $$\frac{3}{4}$$ as a pair of fractions with a common denominator? Type below: _________ Answer: $$\frac{10}{12}$$ and $$\frac{9}{12}$$ Explanation: Sam needs 5/6 cup mashed bananas and 3/4 cup mashed strawberries for a recipe He wants to find whether he needs more bananas or strawberries List the multiples of 6 = 6, 12, 18, 24, 30, 36, 42,….. List the multiples of 4 = 4, 8, 12, 16, 20, 24, …. The common denominator of 6 and 4 is 12 Multiply the numerator and denominator of 5/6 and 3/4 with 12 (5 x 12)/(6 x 12) and (3 x 12)/(4 x 12) 10/12 and 9/12 Pair of fractions with a common denominator for 5/6 and 3/4 are 10/12 and 9/12 Question 15. Karen will divide her garden into equal parts. She will plant corn in $$\frac{8}{12}$$ of the garden. What is the fewest number of parts she can divide her garden into? ______ parts Answer: $$\frac{2}{3}$$ parts Explanation: As per the given data, Keren will divide her garden into equal parts She will plant corn in 8/12 of the garden To get the least number of parts she can divide her garden, simplify the 8/12 Divide the numerator and denominator of 8/12 with 4 (8 ÷ 4)/(12 ÷ 4) = 2/3 So, Karen can divide her garden into 2/3 of parts Question 16. Olivia is making scarves. Each scarf will have 5 rectangles, and $$\frac{2}{5}$$ of the rectangles will be purple. How many purple rectangles does she need for 3 scarves? ______ purple rectangles Answer: 6 purple rectangles Explanation: As per the given data, Olivia is making scarves Each scarf will have 5 rectangles and 2/5 of the rectangles will be purple = 5 x 2/5 = 2 That means each scarf will have 2 purple rectangles For 3 scarves = 3 x 2 = 6 So, she needs 6 purple rectangles. Question 17. Paul needs to buy $$\frac{5}{8}$$ pound of peanuts. The scale at the store measures parts of a pound in sixteenths. What measure is equivalent to $$\frac{5}{8}$$ pound? $$\frac{□}{□}$$ pound of peanuts Answer: $$\frac{10}{16}$$ pound of peanuts Explanation: As per the given data, Paul needs to buy 5/8 pounds of peanuts The scale at the store measures parts of a pound in sixteenths = 16 x 5/8 = 10 To find Equivalent fraction of 5/8 Multiply the numerator and denominator of 5/8 with 2 (5 x 2)/( 8 x 2) = 10/16 So, the equivalent fraction of 5/8 is 10/16 ### Page No. 361 Question 1. Compare $$\frac{2}{5}$$ and $$\frac{1}{8}$$. Write < or >. $$\frac{2}{5}$$ _____ $$\frac{1}{8}$$ Answer: $$\frac{2}{5}$$ > $$\frac{1}{8}$$ Explanation: Least common denominator of 5 and 8 = 40 Multiply the numerator and denominator of 2/5 and 1/8 with 40 2/ 5 = (2 x 8)/(5 x 8) = 16/40 1/8 = (1 x 5)/(8 x 5) = 5/40 The denominators are same now So, compare the numerator to find the greater number 16/40 > 5/40 So, 2/5 > 1/8 Compare. Write < or >. Question 2. $$\frac{1}{2}$$ _____ $$\frac{4}{6}$$ Answer: $$\frac{1}{2}$$ < $$\frac{4}{6}$$ Explanation: 1/2 and 4/6 Least common denominator of 2 and 6 = 6 Multiply the numerator and denominator of 1/2 and 4/6 with 6 1/ 2 = (1 x 6)/(2 x 6) = 6/12 4/ 6 = (4x 2)/(6 x 2) = 8/12 The denominators are same now So, compare the numerator to find the greater number. 6/12 < 8/12 So, 1/2 < 4/6 Question 3. $$\frac{3}{10}$$ _____ $$\frac{1}{2}$$ Answer: $$\frac{3}{10}$$ > $$\frac{1}{2}$$ Explanation: 1 / 10 and 1/2 Least common denominator of 10 and 2 = 10 Multiply the numerator and denominator of 3/10 and 1/2 with 10 3/ 10 = (3 x 2)/(10 x 2) = 6/20 1/2 = (1 x 10)/(2 x 10) = 10/20 The denominators are same now So, compare the numerator to find the greater number. 6/20 < 10/20 So, 3/10 > 1/2 Question 4. $$\frac{11}{12}$$ _____ $$\frac{4}{8}$$ Answer: $$\frac{11}{12}$$ > $$\frac{4}{8}$$ Explanation: 11/12 and 4/8 Least common denominator of 12 and 8 = 24 Multiply the numerator and denominator of 11/12 and 4/8 with 24 11/ 12 = (11 x 8)/(12 x 8) = 88/96 4/8 = (4 x 12)/(8 x 12) = 48/96 The denominators are same now So, compare the numerator to find the greater number 88/96 > 48/96 So, 11/12 > 4/8 Question 5. $$\frac{5}{8}$$ _____ $$\frac{2}{5}$$ Answer: $$\frac{5}{8}$$ > $$\frac{2}{5}$$ Explanation: 5/ 8 and 2/5 Least common denominator of 5 and 8 = 40 Multiply the numerator and denominator of 5/8 and 2/8 with 40 5/ 8 = (5 x 5)/(8 x 5) = 25/40 2/5 = (2 x 8)/(5 x 8) = 16/40 The denominators are same now So, compare the numerator to find the greater number 25/ 40 > 16/40 So, 5/8 > 2/5 Question 6. $$\frac{8}{10}$$ _____ $$\frac{3}{8}$$ Answer: $$\frac{8}{10}$$ > $$\frac{3}{8}$$ Explanation: 8/10 and 3/8 Least common denominator of 10 and 8 = 40 Multiply the numerator and denominator of 8/10 and 3/8 with 40 8/ 10 = (8 x 8)/(10 x 8) = 64/80 3/8 = (3 x 10)/(8 x 10) = 30/80 The denominators are same now So, compare the numerator to find the greater number 64/80 > 30/80 So, 8/10 > 3/8 Question 7. $$\frac{1}{3}$$ _____ $$\frac{7}{12}$$ Answer: $$\frac{1}{3}$$ < $$\frac{7}{12}$$ Explanation: 1/3 and 7/12 Least common denominator of 3 and 12 = 12 Multiply the numerator and denominator of 1/3 and 7/12 with 40. 1/ 3 = (1 x 12)/(3 x 12) = 12/36 7/12 = (7 x 3)/(12 x 3) = 21/36 The denominators are same now So, compare the numerator to find the greater number 12/36 < 21/36 So, 1/3 < 7/12 Question 8. $$\frac{2}{6}$$ _____ $$\frac{7}{8}$$ Answer: $$\frac{2}{6}$$ < $$\frac{7}{8}$$ Explanation: 2/6 and 7/8 Least common denominator of 6 and 8 = 24 Multiply the numerator and denominator of 2/6 and 7/8 with 40 2/ 6 = (2 x 8)/(6 x 8) = 16/48 7/8 = (7 x 6)/(8 x 6) = 42/48 The denominators are same now So, compare the numerator to find the greater number 16/48<42/48 So, 2/6 < 7/8 Question 9. $$\frac{4}{8}$$ _____ $$\frac{2}{10}$$ Answer: $$\frac{4}{8}$$ > $$\frac{2}{10}$$ Explanation: 4/8 and 2/10 Least common denominator of 8 and 10 = 40 Multiply the numerator and denominator of 4/8 and 2/10 with 40 4/ 8 = (4 x 10)/(8 x 10) = 40/80 2/10 = (2 x 8)/(10 x 8) = 16/80 The denominators are same now So, compare the numerator to find the greater number 40/80 > 16/80 So, 4/8 > 2/10 Reason Quantitatively Algebra Find a numerator that makes the statement true. Question 10. $$\frac{2}{4}<\frac { □ }{ 6 }$$ □ = _____ Answer: 4 Explanation: 2/4 < x/6 Least common denominator of 4 and 6 = 12 Multiply the numerator and denominator of 2/4 < x/6 with 40 2/4 = (2 x 6)/(4 x 6) = 12/24 x/6 = (x x 4)/(6 x 4) = 4 x/24 The denominators are same now So, compare the numerator to find the greater number 12/24 < 4 X 4/24 Question 11. $$\frac{8}{10}>\frac { □ }{ 8 }$$ □ = _____ Answer: 1 Explanation: 8/10 < x/8 Least common denominator of 10 and 8 = 40 8/10 = (8 x 4)/(10 x 4) = 32/40 x/8 = (x X 5)/(8 x 5) = 5x/40 The denominators are same now So, compare the numerator to find the greater number 8/10 < 5x/40. X will be 1 Question 12. $$\frac{10}{12}>\frac { □ }{ 4 }$$ □ = _____ Answer: 1 Explanation: 10/12 < x/4 Least common denominator of 12 and 4 = 12 10/12 = (10 x 1)/(12 x 1) = 10/12 x/4 = (x X 3)/(4 x 3) = 3x/12 The denominators are same now So, compare the numerator to find the greater number 10/12 < 3/12. X will be 1. Question 13. $$\frac{2}{5}<\frac { □ }{ 10 }$$ □ = _____ Answer: 5 Explanation: 2/5 < x/10 Least common denominator of 5 and 10 = 10 2/5 = (2x 2)/(5 x 2) = 4/10 x/10 = (x X 1)/(10 x 1) = x/10 The denominators are same now So, compare the numerator to find the greater number 2/5 < 5/10. X will be 5. Question 14. When two fractions are between 0 and $$\frac{1}{2}$$, how do you know which fraction is greater? Explain. Type below: _______ Answer: When two fractions are between 0 and $$\frac{1}{2}$$. $$\frac{1}{2}$$ is greater. As the tenths place of 5 is greater than 0. $$\frac{1}{2}$$ is greater. Question 15. If you know that $$\frac{2}{6}<\frac{1}{2}$$ and $$\frac{3}{4}<\frac{1}{2}$$, what do you know about $$\frac{2}{6} \text { and } \frac{3}{4}$$? Type below: _______ Answer: Explanation: As per the given data, 2/6 < 1/2 and 3/4 < 1/2 Then, 2/6 and 3/4 is The least common denominator of 6 and 4 is 12 (2 x 4)/(6 x 4) and (3 x 6)/(4 x 6) 8/24 and 18/24 Now, the denominators are same, then compare the numerators 8/24 > 18/24 So, 2/6 > 3/4 Question 16. Sandra has ribbons that are $$\frac{3}{4}$$ yard, $$\frac{2}{6}$$ yard, $$\frac{1}{5}$$ yard, and $$\frac{4}{7}$$ yard long. She needs to use the ribbon longer than $$\frac{2}{3}$$ yard to make a bow. Which length of ribbon could she use for the bow? $$\frac{□}{□}$$ yard Answer: Explanation: ### Page No. 362 Question 17. Saundra ran $$\frac{7}{12}$$ of a mile. Lamar ran $$\frac{3}{4}$$ of a mile. Who ran farther? Explain. _______ Answer: As per the given data, Saundra ran 7/12 of a mile Lamar ran 3/4 of a mile The least common denominator of 7/12 and 3/4 is 12 (7x 1)/( 12 x 1) and ( 3 x 3 )/( 4 x 3) 7/12 and 9/12 So, 7/12 < 9/12 So, 7/12 < 3/4 Lamar ran greater distance than Saundra Question 18. What’s the Question? Selena ran farther than Manny. Type below: _______ Answer: Who ran farther? Selena or Manny Question 19. Chloe made a small pan of ziti and a small pan of lasagna. She cut the ziti into 8 equal parts and the lasagna into 9 equal parts. Her family ate $$\frac{2}{3}$$ of the lasagna. If her family ate more lasagna than ziti, what fraction of the ziti could have been eaten? Type below: _______ Answer: $$\frac{1}{4}$$ Explanation: As per the given data, Chloe made a small pan of ziti and a small pan of lasagna She cut the ziti into 8 equal parts and the lasagna into 9 equal parts Her family ate 2/3 of the lasagna = (2/3) x 9 = 6 parts If her family ate more lasagna than ziti, then that is less than 6 parts So, 1/4 of the ziti = (1/4) x 8 = 2 parts So, 1/4 of ziti eaten by Chloe family Question 20. James, Ella, and Ryan biked around Eagle Lake. James biked $$\frac{2}{10}$$ of the distance in an hour. Ella biked $$\frac{4}{8}$$ of the distance in an hour. Ryan biked $$\frac{2}{5}$$ of the distance in an hour. Compare the distances biked by each person by matching the statements to the correct symbol. Each symbol may be used more than once or not at all. Type below: _______ Answer: 2/10 < 4/8 1 / 8 > 2/5 2/10 < 2/5 Explanation: As per the given data, James, Ella, and Ryan biked around eagle lake James biked 2/10 of the distance in an hour Ella biked 4/8 of the distance in an hour Ryan biked 2/5 of the distance in an hour Least common denominator of 2 /10, 4/8, and 2/5 is 40 (2x 4)/(10 x 4), (4 x 5)/(8 x 5), and (2 x 8)/(5 x 8) 8/40, 20/ 40, and 16/ 40 8/40 < 16/40 < 20/40 2/10 < 2/5 < 4/8 So, 2/10 < 4/8 1 / 8 > 2/5 2/10 < 2/5 ### Common Core – Compare Fractions Using Benchmarks – Page No. 363 Compare. Write < or > . Question 1. Answer: $$\frac{1}{8}$$ < $$\frac{6}{10}$$ Explanation: Question 2. $$\frac{4}{12}$$ _______ $$\frac{4}{6}$$ Answer: $$\frac{4}{12}$$ < $$\frac{4}{6}$$ Explanation: 4/12 and 4/6 4/12 is less than 1/2 4/6 is greater than 1/2 So, 4/12 < 4/6 Question 3. $$\frac{2}{8}$$ _______ $$\frac{1}{2}$$ Answer: $$\frac{2}{8}$$ < $$\frac{1}{2}$$ Explanation: 2/8 and 1/2 2/8 is less than 1/2 1/2 is equal to 1/2 So, 2/8 < 1/2 Question 4. $$\frac{3}{5}$$ _______ $$\frac{3}{3}$$ Answer: $$\frac{3}{5}$$ < $$\frac{3}{3}$$ Explanation: 3/5 and 3/3 3/5 is greater than 1/2 3/3 is equal to 1 So, 3/5 < 3/3 Question 7. $$\frac{4}{6}$$ _______ $$\frac{7}{8}$$ Answer: $$\frac{4}{6}$$ < $$\frac{7}{8}$$ Explanation: 4/6 and 7/8 4/6 is greater than 1/2 7/8 is closer to 1 So, 4/6 < 7/8 Question 8. $$\frac{2}{4}$$ _______ $$\frac{2}{3}$$ Answer: $$\frac{2}{4}$$ < $$\frac{2}{3}$$ Explanation: 2/4 and 2/3 2/4 is equal to 1/2 2/3 is greater than 1/2 So, 2/4 < 2/3 Question 9. $$\frac{3}{5}$$ _______ $$\frac{1}{4}$$ Answer: $$\frac{3}{5}$$ > $$\frac{1}{4}$$ Explanation: 3/5 and 1/4 3/5 is greater than 1/2 1/4 is less than 1/2 So, 1/4 < 3/5 Question 10. $$\frac{6}{10}$$ _______ $$\frac{2}{5}$$ Answer: $$\frac{6}{10}$$ > $$\frac{2}{5}$$ Explanation: 6/10 and 2/5 6/10 is greater than 1/2 2/5 is less than 1/2 So, 2/5 < 6/10 Question 11. $$\frac{1}{8}$$ _______ $$\frac{2}{10}$$ Answer: $$\frac{1}{8}$$ < $$\frac{2}{10}$$ Explanation: 1/8 and 2/10 1/8 is less than 1/2 2/10 is less than 1/2 but greater than 1/8 So, 1/8 < 2/10 Question 12. $$\frac{2}{3}$$ _______ $$\frac{5}{12}$$ Answer: $$\frac{2}{3}$$ > $$\frac{5}{12}$$ Explanation: 2/3 and 5/12 2/3 is greater than 1/2 5/12 is less than 1/2 So, 5/12 < 2/3 Question 13. $$\frac{4}{5}$$ _______ $$\frac{5}{6}$$ Answer: $$\frac{4}{5}$$< $$\frac{5}{6}$$ Explanation: 4/5 and 5/6 4/5 is greater than 1/2 5/6 is greater than 1/2 Common denominator is 30 (4×6)/(5×6) and (5×5)/(6×5) 24/30 and 25/30 24/30 < 25/30 So, 4/5 < 5/6 Question 14. $$\frac{3}{5}$$ _______ $$\frac{5}{8}$$ Answer: $$\frac{3}{5}$$ < $$\frac{5}{8}$$ Explanation: 3/5 and 5/8 3/5 is greater than 1/2 5/8 is greater than 1/2 Common denominator is 40 (3×8)/(5×8) and (5×5)/(8×5) 24/40 and 25/ 40 24/40 < 25/40 3/5 < 5/8 Question 15. $$\frac{8}{8}$$ _______ $$\frac{3}{4}$$ Answer: $$\frac{8}{8}$$ > $$\frac{3}{4}$$ Explanation: 8/8 and 3/4 8/8 is equal to 1 3/4 is less than 1 3/4 < 8/8 ### Common Core – Compare Fractions Using Benchmarks – Page No. 364 Question 1. Which symbol makes the statement true? Options: a. > b.< c. = d. none Answer: a. > Explanation: 4/6 ? 3/8 By comparing 4/6 with 1/2, 4/6 > 1/2 By comparing 3/8 with 1/2, 3/8 < 1/2 So, 4/6 > 3/8 Question 2. Which of the following fractions is greater than $$\frac{3}{4}$$? Options: a. $$\frac{1}{4}$$ b. $$\frac{5}{6}$$ c. $$\frac{3}{8}$$ d. $$\frac{2}{3}$$ Answer: b. $$\frac{5}{6}$$ Explanation: From the given data, By comparing the 3/4 with 1/2, 3/4 > 1/2 Same as above, compare the options with ½ a. 1/4 < 1/2 b. 5/6 > 1/2 c. 3/8 < 1/2 d. 2/3 > 1/2 5/6 and 2/3 are greater than the 1/2 So, compare the 5/6 with 2/3 Then, 5/6 > 2/3 So, 5/6 > 3/4 Question 3. Abigail is putting tiles on a table top. She needs 48 tiles for each of 8 rows. Each row will have 6 white tiles. The rest of the tiles will be purple. How many purple tiles will she need? Options: a. 432 b. 384 c. 336 d. 48 Answer: c. 336 Explanation: As per the given data Abigail is putting tiles on a tabletop Number of rows = 8 She needs 48 tiles for each row = 48×8 = 384 Number of white tiles per row = 6×8 = 48 Rest of the tiles will be purple = 384 – 48 =336 So, the total number of purple color tiles = 336 Question 4. Each school bus going on the field trip holds 36 students and 4 adults. There are 6 filled buses on the field trip. How many people are going on the field trip? Options: a. 216 b. 240 c. 256 d. 360 Answer: b. 240 Explanation: From the given data, Each school bus going on the field trip holds 36 students and 4 adults There are 6 filled buses on the field trip 6 x (36 + 4) = 6 x 40 = 240 So, the total number of people on the field trip = 240 Question 5. Noah wants to display his 72 collector’s flags. He is going to put 6 flags in each row. How many rows of flags will he have in his display? Options: a. 12 b. 15 c. 18 d. 21 Answer: a. 12 Explanation: As mentioned in the data, Noah wants to display his 72 collector’s flag He is going to put 6 flags in each row = 6x = 72 X = 12 So, total 12 number of rows of flags will have in his display Question 6. Julian wrote this number pattern on the board: 3, 10, 17, 24, 31, 38. Which of the numbers in Julian’s pattern are composite numbers? Options: a. 3, 17, 31 b. 10, 24, 38 c. 10, 17, 38 d. 17, 24, 38 Answer: b. 10, 24, 38 Explanation: As per the given information Julian wrote his number pattern on the board =3, 10, 17, 24, 31, 38 Factors of 3 = 1,3 Factors of 10 = 1,2,5,10 Factors of 17 = 1, 17 Factors of 24 = 1, 2, 3, 4, 6 Factors of 31 = 1, 31 Factors of 38 = 1, 2, 19, 38 So, the composite number is 10, 24, and 38, which numbers have more than 2 factors ### Page No. 367 Question 1. Compare $$\frac{2}{5}$$ and $$\frac{1}{10}$$. Think: Use ______ as a common denominator. $$\frac{2}{5}=\frac { □×□ }{ □×□ }$$ = $$\frac{□}{□}$$ $$\frac{1}{10}$$ Think: 4 tenth-size parts 1 tenth-size part. $$\frac{2}{5}$$ _____ $$\frac{1}{10}$$ Answer: $$\frac{2}{5}$$ > $$\frac{1}{10}$$ Explanation: Compare 2/5 and 1/10 Think: 10 as common denominator Multiply the numerator and denominator of 2/5 with 2 Then, (2×2) ÷ (5×2) = 4/10 Now, compare the 4/10 with 1/10 4/10 > 1/10 So, 2/5 > 1/10 Question 2. Compare $$\frac{6}{10}$$ and $$\frac{3}{4}$$. Think: Use ______ as a common denominator. $$\frac{6}{10}$$ $$\frac{3}{4}=\frac { □×□ }{ □×□ }$$ = $$\frac{□}{□}$$ Think: A tenth-size part an eighth-size part. $$\frac{6}{10}$$ _____ $$\frac{3}{4}$$ Answer: $$\frac{6}{10}$$ < $$\frac{3}{4}$$ Explanation: Compare 6/10 and 3/4 Think: Use 40 as a common denominator So, multiply the denominator and numerator of 3/4 with 10 That is, (3×10) ÷ (4×10) = 30/40 Multiply the numerator and denominator of 6/10 with 4 That is, (6×4) ÷ (10×4) = 24/40 Denominators are same, compare the numerator values of 24/40 and 30/40 So, 24/40 < 30/40 Then, 6/10 < 3/4 Compare. Write <, >, or =. Question 3. $$\frac{7}{8}$$ _____ $$\frac{2}{8}$$ Answer: $$\frac{7}{8}$$ > $$\frac{2}{8}$$ Explanation: Compare 7/8 and 2/8 Denominator values are same but numerator values are different Now, compare the numerator values of 7/8 and 2/8 Then, 7/8 > 2/8 Question 4. $$\frac{5}{12}$$ _____ $$\frac{3}{6}$$ Answer: $$\frac{5}{12}$$ < $$\frac{3}{6}$$ Explanation: Compare 5/12 and 3/6 Multiply the numerator and denominator of 3/6 with 2 (3×2) ÷ (6×2) = 6/12 So, 5/12 < 6/12 Question 5. $$\frac{4}{10}$$ _____ $$\frac{4}{6}$$ Answer: $$\frac{4}{10}$$ < $$\frac{4}{6}$$ Explanation: Compare 4/10 and 4/6 Multiply the numerator and denominator of 4/6 with 10 (4×10) ÷ (6×10) = 40/60 Multiply the numerator and denominator of 4/10 with 6 (4×6) ÷ (10×6) = 24/60 So, 24/60 < 40/60 Then, 4/10 < 4/6 Question 6. $$\frac{6}{12}$$ _____ $$\frac{2}{4}$$ Answer: $$\frac{6}{12}$$ = $$\frac{2}{4}$$ Explanation: Compare 6/12 and 2/4 Multiply the numerator and denominator of 2/4 with 3 (2×3) ÷ (4×3) = 6/12 So, 6/12 = 6/12 Then, 6/12 = 2/4 Question 7. $$\frac{1}{3}$$ _____ $$\frac{1}{4}$$ Answer: $$\frac{1}{3}$$ < $$\frac{1}{4}$$ Explanation: Compare 1/3 and 1/4 Multiply the numerator and denominator of 1/3 with 4 (1×4) ÷ (3×4) = 4/12 Multiply the numerator and denominator of 1/4 with 3 (1×3) ÷ (4×3) = 3/12 So, 4/12 < 3/12 Then, 1/3 < 1/4 Question 8. $$\frac{4}{5}$$ _____ $$\frac{8}{10}$$ Answer: $$\frac{4}{5}$$ = $$\frac{8}{10}$$ Explanation: Compare 4/5 and 8/10 Multiply the numerator and denominator of 4/5 with 2 (4×2) ÷ (5×2) = 8/10 So, 8/10 = 8/10 Then, 4/5 = 8/10 Question 9. $$\frac{3}{4}$$ _____ $$\frac{2}{6}$$ Answer: $$\frac{3}{4}$$ < $$\frac{2}{6}$$ Explanation: Compare 3/4 and 2/6 Multiply the numerator and denominator of 3/4 with 6 (3×6) ÷ (4×6) = 18/24 Multiply the numerator and denominator of 2/6 with 4 (2×4) ÷ (6×4) = 8/24 So, 18/24 < 8/24 Then, 3/4 < 2/6 Question 10. $$\frac{1}{2}$$ _____ $$\frac{5}{8}$$ Answer: $$\frac{1}{2}$$ < $$\frac{5}{8}$$ Explanation: Compare 1/2 and 5/8 Multiply the numerator and denominator of 1/2 with 4 (1×4) ÷ (2×4) = 4/8 So, 4/8 < 5/8 Then, 1/2 < 5/8 Reason Quantitatively Algebra Find a number that makes the statement true. Question 11. $$\frac{1}{2}>\frac { □ }{ 3 }$$ □ = ______ Answer: 1 Explanation: 1/2 > x/3 Multiply the numerator and denominator of 1/2 with 3 (1×3) ÷ (2×3) = 3/6 Multiply the numerator and denominator of x/3 with 2 (Xx2) ÷ (3×2) = 2x/6 3/6 > 2x/6 So, x= 1 Then, 3/6 > 2/6 1/2 > 1/3 Question 12. $$\frac{3}{10}>\frac { □ }{ 5 }$$ □ = ______ Answer: 1 Explanation: 3/10 > x/5 Multiply the numerator and denominator of x/5 with 2 (Xx2) ÷ (5×2) =2x/10 3/10 > 2x/10 So, x=1 3/10 > 2/10 3/10 > 1/5 Question 13. $$\frac{5}{12}>\frac { □ }{ 3 }$$ □ = ______ Answer: 1 Explanation: 5/12 > x/3 Multiply numerator and denominator of x/3 with 4 (Xx4) ÷(3×4) = 4x/12 5/12 > 4x/12 So, x = 1 Then, 5/12 > 4/12 5/12 > 1/3 Question 14. $$\frac{2}{3}>\frac { 4 }{ □ }$$ □ = ______ Answer: Explanation: Question 15. Students cut a pepperoni pizza into 12 equal slices and ate 5 slices. They cut a veggie pizza into 6 equal slices and ate 4 slices. Use fractions to compare the amounts of each pizza that were eaten. Type below: _________ Answer: $$\frac{5}{12}$$ < $$\frac{4}{6}$$ Explanation: As per the given data, Students cut a pepperoni pizza into 12 equal slices and ate 5 slices =5/12 They cut veggie pizza into 6 equal slices and ate 4 slices = 4/6 Compare 5/12 and 4/6 Multiply the numerator and denominator of 4/6 with 2 (4×2) ÷ (6×2) = 8/12 So, 5/12 < 8/12 Then, 5/12 < 4/6 ### Page No. 368 Question 16. Jerry is making a strawberry smoothie. Which measure is greatest, the amount of milk, cottage cheese, or strawberries? a. What do you need to find? Type below: _________ Answer: I need to find the greatest measure from milk, cottage cheese, or strawberries Question 16. b. How will you find the answer? Type below: _________ Answer: Equal the denominators of 3/4, 2/6, and 8/12 Multiply the numerator and denominator of 3/4 with 3 (3×3) ÷ (4×3) = 9/12 Multiply the numerator and denominator of 2/6 with 2 (2×2) ÷ (6×2) = 4/12 Compare 4/12 < 8/12 < 9/12 So, 2/6 < 8/12 <3/4 Question 16. c. Show your work. Type below: _________ Answer: 2/6 < 8/12 < 3/4 Question 16. d. Jerry needs more ________ than the other two ingredients. ________ Answer: Jerry needs more strawberries than the other two ingredients Question 17. Angie, Blake, Carlos, and Daisy went running. Angie ran $$\frac{1}{3}$$ mile, Blake ran $$\frac{3}{5}$$ mile, Carlos ran $$\frac{7}{10}$$ mile, and Daisy ran $$\frac{1}{2}$$ mile. Which runner ran the shortest distance? Who ran the greatest distance? The shortest distance: ________ The greatest distance: ________ Answer: The shortest distance: $$\frac{1}{3}$$ The greatest distance: $$\frac{7}{10}$$ Explanation: As per the given data, Angie, Blake, Carlos, and Daisy went running Angie ran 1/3 mile, Blake ran 3/5 mile, Carlos ran 7/10 mile, and Daisy ran 1/2 mile Least common denominator of 1/3, 3/5, 7/10, and 1/2 =30 (1x 10)/(3×10), (3×6)/(5×6), (7×3)/(10×3), (1×15)/(2×15) 10/30, 18/30, 21/30, 15/30 10/30 < 15/30 < 18/30 < 21/30 1/3 < 1/2 < 3/5 < 7/10 The shortest distance ran by Angie and is 1/ 3 The greatest distance ran by Carlos and is 7/10 Question 18. Elaine bought $$\frac{5}{8}$$ pound of potato salad and $$\frac{4}{6}$$ pound of macaroni salad for a picnic. Use the numbers to compare the amounts of potato salad and macaroni salad Elaine bought. Type below: _________ Answer: As per the given data, Elaine bought 5/8 pound of potato salad and 4/6 pound of macaroni salad for a picnic Multiply the numerator and denominator of 5/8 with 6 (5×6) / (8×6) = 30/48 Multiply the numerator and denominator of 4/6 with 8 (4×8) / (6×8) = 32/48 30/48 < 32/48 So, 5/8 < 4/6 Elaine bought more macaroni salad than potato salad ### Common Core – Compare Fractions – Page No. 369 Compare. Write <, >, or = Question 1. Answer: $$\frac{1}{5}$$ < $$\frac{2}{10}$$ Explanation: Question 2. $$\frac{1}{5}$$ _____ $$\frac{2}{10}$$ Answer: $$\frac{1}{5}$$ = $$\frac{2}{10}$$ Explanation: 1/5 and 2/10 Think: 10 is a common denominator 1/5 = (1×2) / (5×2) = 2/10 2/10 = 2/10 So, 1/5 = 2/10 Question 3. $$\frac{2}{4}$$ _____ $$\frac{2}{5}$$ Answer: $$\frac{2}{4}$$ > $$\frac{2}{5}$$ Explanation: 2/4 and 2/5 20 is a common denominator 2/4 = (2×5)/(4×5) = 10/20 2/5 = (2×4)/(5×4) = 8/20 10/20 > 8/20 So, 2/4 > 2/5 Question 4. $$\frac{3}{5}$$ _____ $$\frac{7}{10}$$ Answer: $$\frac{3}{5}$$ < $$\frac{7}{10}$$ Explanation: 3/5 and 7/10 10 is a common denominator 3/5 = (3×2)/(5×2) = 6/10 7/10 6/10 < 7/10 So, 3/5 < 7/10 Question 7. $$\frac{1}{3}$$ _____ $$\frac{2}{4}$$ Answer: $$\frac{1}{3}$$ < $$\frac{2}{4}$$ Explanation: 1/3 and 2/4 12 is a common denominator 1/3 = (1×4)/(3×4) = 4/12 2/4 = (2×3)/(4×3) = 6/12 4/12 < 6/12 So, 1/3 < 2/4 Question 8. $$\frac{2}{5}$$ _____ $$\frac{1}{2}$$ Answer: $$\frac{2}{5}$$ < $$\frac{1}{2}$$ Explanation: 2/5 and 1/2 10 is a common denominator 2/5 = (2×2)/(5×2) = 4/10 1/2 = (1×5)/(2×5) = 5/10 4/10 < 5/10 So, 2/5 < 1/2 Question 9. $$\frac{4}{8}$$ _____ $$\frac{2}{4}$$ Answer: $$\frac{4}{8}$$ = $$\frac{2}{4}$$ Explanation: 4/8 and 2/4 8 is a common denominator 4/8 2/4 = (2×2)/(4×2) = 4/8 2/4 = 4/8 So, 4/8 = 2/4 Question 10. $$\frac{7}{12}$$ _____ $$\frac{2}{4}$$ Answer: $$\frac{7}{12}$$ < $$\frac{2}{4}$$ Explanation: 7/12 and 2/4 12 is a common denominator 7/12 2/4 = (2×3)/(4×3) = 6/12 7/12 < 6/12 So, 7/12 < 2/4 Question 11. $$\frac{1}{8}$$ _____ $$\frac{3}{4}$$ Answer: $$\frac{1}{8}$$ < $$\frac{3}{4}$$ Explanation: 1/8 and 3/4 8 is a common denominator 1/8 3/4 = (3×2)/(4×2) = 6/8 1/8 < 6/8 So, 1/8 < 3/4 ### Common Core – Compare Fractions – Page No. 370 Question 1. Pedro fills a glass $$\frac{2}{4}$$ full with orange juice. Which of the following fractions is greater than $$\frac{2}{4}$$? Options: a. $$\frac{3}{8}$$ b. $$\frac{4}{6}$$ c. $$\frac{5}{12}$$ d. $$\frac{1}{3}$$ Answer: b. $$\frac{4}{6}$$ Explanation: $$\frac{4}{6}$$ > $$\frac{2}{4}$$ Question 2. Today Ian wants to run less than $$\frac{7}{12}$$ mile. Which of the following distances is less than $$\frac{7}{12}$$ mile? Options: a. $$\frac{3}{4}$$ mile b. $$\frac{2}{3}$$ mile c. $$\frac{5}{6}$$ mile d. $$\frac{2}{4}$$ mile Answer: d. $$\frac{2}{4}$$ mile Explanation: $$\frac{2}{4}$$ is less than $$\frac{7}{12}$$ Question 3. Ms. Davis traveled 372,645 miles last year on business. What is the value of 6 in 372,645? Options: a. 6 b. 60 c. 600 d. 6,000 Answer: c. 600 Explanation: Ms. Davis traveled 372, 645 miles last year on business The value of 6 in 372,645 is 600 Question 4. One section of an auditorium has 12 rows of seats. Each row has 13 seats. What is the total number of seats in that section? Options: a. 25 b. 144 c. 156 d. 169 Answer: c. 156 Explanation: From the given information One section of an auditorium has 12 rows of seats Each row has 13 seats = 13×12 = 156 seats So, the total number of seats in the auditorium = 156 seats Question 5. Sam has 12 black-and-white photos and 18 color photos. He wants to put the photos in equal rows so each row has either black-and-white photos only or color photos only. In how many rows can Sam arrange the photos? Options: a. 1, 2, 3, or 6 rows b. 1, 3, 6, or 9 rows c. 1, 2, or 4 rows d. 1, 2, 3, 4, 6, or 9 rows Answer: a. 1, 2, 3, or 6 rows Explanation: As per the given information Sam has 12 black and white photos 18 color photos He wants to put the photos in equal rows So each row has either black and white photos only or color photos only H.C.F of 12 and 18 is 6 Rows of 6. 2 rows of black equal 12. 3 rows of white equals 18. Question 6. The teacher writes $$\frac{10}{12}$$ on the board. He asks students to write the fraction in simplest form. Who writes the correct answer? Options: a. JoAnn writes $$\frac{10}{12}$$ b. Karen writes $$\frac{5}{12}$$ c. Lynn writes $$\frac{6}{5}$$ d. Mark writes $$\frac{5}{6}$$ Answer: d. Mark writes $$\frac{5}{6}$$ Explanation: As per the given data, The teacher writes 10/12 on the board He asks students to write the fraction in simplest form For the simplest form of 10/12, divide the 10/12 with 2 (10÷2)/(12÷2) = 5/6 5/6 is the simplest form of 10/12 So, Mark writes the correct answer ### Page No. 373 Question 1. Locate and label points on the number line to help you write $$\frac{3}{10}, \frac{11}{12}, \text { and } \frac{5}{8}$$ in order from least to greatest. Type below: ___________ Answer: Explanation: 3/10, 11/12, 5/8 3/10 is closer to 0 11/12 is closer to 1 5/8 is closer to 1/2 So, 3/10 < 5/8 < 11/12 Write the fraction with the greatest value. Question 2. $$\frac{7}{10}, \frac{1}{5}, \frac{9}{10}$$ $$\frac{□}{□}$$ Answer: $$\frac{9}{10}$$ Explanation: 7/10, 1/5, and 9/10 7/10 is closer to 1/2 1/5 is closer to 0 9/10 is closer to 1 So, 9/10 > 7/10 > 1/5 Greatest value is 9/10 Question 3. $$\frac{5}{6}, \frac{7}{12}, \frac{7}{10}$$ $$\frac{□}{□}$$ Answer: $$\frac{5}{6}$$ Explanation: 7/12 is less than 1/2 7/10 and 5/6 are greater than 1/2 Compare 5/6 and 7/12 Multiply the numerator and denominator of 5/6 with 2 (5×2)/(6×2) = 10/12 > 7/12 So, 5/6 > 7/12 Compare 5/6 and 7/10 Multiply the 5/6 with 10 (5×10)/(6×10) = 50/60 Multiply the 7/10 with 6 (7×6)/(10×6) = 42/60 So, 5/6> 7/10 So, 7/12 <7/10<5/6 Question 4. $$\frac{2}{8}, \frac{1}{8}, \frac{2}{4}, \frac{2}{6}$$ $$\frac{□}{□}$$ Answer: $$\frac{2}{4}$$ Explanation: 2/8, 1/8, 2/4, 2/6 Common denominator of 4,6,8 = 24 (2×3)/(8×3), (1×3)/(8×3), (2×6)/(4×6), (2×4)/(6×4) 6/24, 3/24, 12/24, 8/24 Compare the numerator values 12/24 > 8/24 > 6/24 > 3/24 So, 2/4 > 2/6 > 2/8 >1/8 Write the fractions in order from least to greatest. Question 7. $$\frac{3}{4}, \frac{7}{12}, \frac{5}{12}$$ $$\frac{□}{□}$$ Type below: ________ Answer: $$\frac{5}{12}, \frac{7}{12}, \frac{3}{4}$$ Explanation: 3/4, 7/12, 5/12 3/ 4 is closer to 1 7/12 is greater than 1/2 5/ 12 is closer to 1/2 So, 5/12 < 7/12 < 3/4 Write the fractions in order from least to greatest. Question 8. $$\frac{2}{5}, \frac{1}{3}, \frac{5}{6}$$ $$\frac{□}{□}$$ Type below: ________ Answer: $$\frac{1}{3}, \frac{2}{5}, \frac{5}{6}$$ Explanation: 2/5, 1/3, 5/6 2/5 is closer to 1/2 1/3 is closer to 0 5/6 is closer to 1 So, 1/3 < 2/5 < 5/6 Question 9. $$\frac{4}{8}, \frac{5}{12}, \frac{1}{6}$$ $$\frac{□}{□}$$ Type below: ________ Answer: $$\frac{1}{6}, \frac{5}{12}, \frac{4}{8}$$ Explanation: 4/8, 5/12, 1/6 4/8 is equal to1/2 5/12 is closer to 1/2 1/6 is closer to 0 So, 1/6 < 5/12 < 4/ 8 Question 10. $$\frac{7}{100}, \frac{9}{10}, \frac{4}{5}$$ $$\frac{□}{□}$$ Type below: ________ Answer: $$\frac{7}{100}, \frac{4}{5}, \frac{9}{10}$$ Explanation: 7/100, 9/10, 4/5 7/100 is closer to 0 9/10 is closer to 1 4/5 is greater than 1/2 So, 7/100 < 4/5 < 9/10 Reason Quantitatively Algebra Write a numerator that makes the statement true. Question 11. $$\frac{1}{2}<\frac { □ }{ 10 } <\frac{4}{5}$$ □ = _____ Answer: 6 or 7 Explanation: 1/2 < x/10 < 4/5 Common denominator is 10 (1×5)/(2×5) < x/10 < (4×2)/(5×2) 5/10 < x/10 < 8/10 Then, x = 6 or 7 Question 12. $$\frac{1}{4}<\frac{5}{12}<\frac { □ }{ 6 }$$ □ = _____ Answer: 6 Explanation: 1/4 < 5/12 < x/6 Common denominator is 24 (1×6)/(4×6) < (5×2)/(12×2) < 4x/(6×4) 6/24 < 10/24 < 4x/24 If x = 6, then 4x = 24 So, 6/24 < 10/24 < 24/24 Question 13. $$\frac { □ }{ 8 } <\frac{3}{4}<\frac{7}{8}$$ □ = _____ Answer: 1,2,3,4,5 Explanation: x/8 < 3/4 < 7/8 Common denominator is 8 x/8 < (3×2)/(4×2) < 7/8 x/8 < 6/8 < 7/8 so x = 1,2,3,4,5 ### Page No. 374 Question 14. Nancy, Lionel, and Mavis ran in a 5-kilometer race. The table shows their finish times. In what order did Nancy, Lionel, and Mavis finish the race? a. What do you need to find? Answer: In which Nancy, Lionel, and Mavis finished the race? Question 14. b. What information do you need to solve the problem? Type below: _________ Answer: the amount of time it took each runner to finish the race Question 14. c. What information is not necessary? Type below: _________ Answer: the distance of the race Question 14. d. How will you solve the problem? Type below: _________ Answer: By using the running race time of Nancy, Lionel, and Mavis Question 14. e. Show the steps to solve the problem. Type below: _________ Answer: Common denominator of 2/3, 7/12, 3/4 is 12 (2×4)/(3×4), (7/12), (3×3)/(4×3) 8/12, 7/12, 9/12 7/12 < 8/12 < 9/12 7/12 < 2/3 < 3/4 Lionel < Nancy < Mavis Question 14. f. Complete the sentences. The runner who finished first is _______. The runner who finished second is _______. The runner who finished third is _______. The first: _______ The second: _______ The third: _______ Answer: Lionel finished the race first Nancy finished the race second Mavis finished the race third Lionel Nancy Mavis ### Common Core – Compare and Order Fractions – Page No. 375 Write the fractions in order from least to greatest. Question 1. $$\frac{5}{8}, \frac{2}{12}, \frac{8}{10}$$ Answer: $$\frac{2}{12}, \frac{5}{8}, \frac{8}{10}$$ Explanation: Question 2. $$\frac{1}{5}, \frac{2}{3}, \frac{5}{8}$$ Type below: _________ Answer: $$\frac{1}{5}, \frac{5}{8}, \frac{2}{3}$$ Explanation: 1/5, 2/3, 5/8 1/5 is closer to 0 2/3 is greater than 1/2 5/8 greater than 1/2 1/5 < 5/8 < 2/3 Question 3. $$\frac{1}{2}, \frac{2}{5}, \frac{6}{10}$$ Type below: _________ Answer: $$\frac{2}{5}, \frac{1}{2}, \frac{6}{10}$$ Explanation: 1/2, 2/5, 6/10 1/2 is equal to 1/2 2/5 is less than 1/2 6/10 is greater than 1/2 Question 4. $$\frac{4}{6}, \frac{7}{12}, \frac{5}{10}$$ Type below: _________ Answer: $$\frac{5}{10}$$ < $$\frac{7}{12}$$ < $$\frac{4}{6}$$ Explanation: 4/6, 7/12, 5/10 4/6 is closer to 1 7/12 is greater than 1/2 5/10 is equal to 1/2 Question 5. $$\frac{1}{4}, \frac{3}{6}, \frac{1}{8}$$ Type below: _________ Answer: $$\frac{1}{8}$$ < $$\frac{1}{4}$$ < $$\frac{3}{6}$$ Explanation: 1/4, 3/6, 1/8 1/4 is less than 1/2 3/6 is equal to 1/2 1/8 is closer to 0 Question 6. $$\frac{1}{8}, \frac{3}{6}, \frac{7}{12}$$ Type below: _________ Answer: $$\frac{1}{8}$$ < $$\frac{7}{12}$$ < $$\frac{3}{6}$$ Explanation: 1/8, 3/6, 7/12 1/8 is closer to 0 3/6 is equal to 1/2 7/12 is greater than 1/2 Question 7. $$\frac{8}{100}, \frac{3}{5}, \frac{7}{10}$$ Type below: _________ Answer: $$\frac{8}{100}$$ < $$\frac{3}{5}$$ < $$\frac{7}{10}$$ Explanation: 8/100, 3/5, 7/10 8/100 is closer to 0 3/5 is greater than 1/2 7/10 is closer to 1 Question 8. $$\frac{3}{4}, \frac{7}{8}, \frac{1}{5}$$ Type below: _________ Answer: $$\frac{1}{5}$$ < $$\frac{3}{4}$$ < $$\frac{7}{8}$$ Explanation: 3/4, 7/8, 1/5 3/4 is greater than 1/2 7/8 is closer to 1 1/5 is closer to 0 Question 9. Amy’s math notebook weighs $$\frac{1}{2}$$ pound, her science notebook weighs $$\frac{7}{8}$$ pound, and her history notebook weighs $$\frac{3}{4}$$ pound. What are the weights in order from lightest to heaviest? Type below: _________ Answer: $$\frac{1}{2}$$ pound, $$\frac{3}{4}$$ pound, $$\frac{7}{8}$$ pound Explanation: From the given data, Amy’s math notebook weighs 1/2 pound Science notebook weighs 7/8 pound History notebook weighs 3/4 pound 7/8 is closer to 1 3/4 is greater than 1/2 1/2 < 3/4 < 7/8 So, Amy’s math notebook weight < history notebook weight < science notebook Question 10. Carl has three picture frames. The thicknesses of the frames are $$\frac{4}{5}$$ inch, $$\frac{3}{12}$$ inch, and $$\frac{5}{6}$$ inch. What are the thicknesses in order from least to greatest? Type below: _________ Answer: $$\frac{3}{12}$$ inch, $$\frac{4}{5}$$ inch, $$\frac{5}{6}$$ inch Explanation: As per the given data, Carl has three picture frames The thickness of the frames are 4/5 inch, 3/12 inch, 5/6 inch 4/5 is greater than 1/2 3/12 is less than 1/2 5/6 is closer to 1 3/12 < 4/5 < 5/6 ### Common Core – Compare and Order Fractions – Page No. 376 Question 1. Juan’s three math quizzes this week took him $$\frac{1}{3}$$ hour, $$\frac{4}{6}$$ hour, and $$\frac{1}{5}$$ hour to complete. Which list shows the lengths of time in order from least to greatest? Options: a. $$\frac{1}{3}$$ hour, $$\frac{4}{6}$$ hour, $$\frac{1}{5}$$ hour b. $$\frac{1}{5}$$ hour, $$\frac{1}{3}$$ hour, $$\frac{4}{6}$$ hour c. $$\frac{1}{3}$$ hour, $$\frac{1}{5}$$ hour, $$\frac{4}{6}$$ hour d. $$\frac{4}{6}$$ hour, $$\frac{1}{3}$$ hour, $$\frac{1}{5}$$ hour Answer: b. $$\frac{1}{5}$$ hour, $$\frac{1}{3}$$ hour, $$\frac{4}{6}$$ hour Explanation: From the given information Juan’s three math quizzes this week took him 1/3 hour, 4/6 hour, and 1/5 hour Compare 1/3 and 1/2 1/3 is less than 1/2 4/6 is greater than 1/2 1/5 is closer to 0 1/5 < 1/3 < 4/6 So, Juan’s math quizzes times from least to greatest is 1/5, 1/3, 4/6 Question 2. On three days last week, Maria ran $$\frac{3}{4}$$ mile, $$\frac{7}{8}$$ mile, and $$\frac{3}{5}$$ mile. What are the distances in order from least to greatest? Options: a. $$\frac{3}{4}$$ mile, $$\frac{7}{8}$$ mile, $$\frac{3}{5}$$ mile b. $$\frac{3}{5}$$ mile, $$\frac{3}{4}$$ mile, $$\frac{7}{8}$$ mile c. $$\frac{7}{8}$$ mile, $$\frac{3}{4}$$ mile, $$\frac{3}{5}$$ mile d. $$\frac{7}{8}$$ mile, $$\frac{3}{5}$$ mile, $$\frac{3}{4}$$ mile Answer: b. $$\frac{3}{5}$$ mile, $$\frac{3}{4}$$ mile, $$\frac{7}{8}$$ mile Explanation: As per the information On three days last week, Maria ran 3/4 mile, 7/8 mile, and 3/5 mile 3/4 is greater than 1/2 7/8 is closer to 1 3/5 is greater than 1/2 Compare 3/5 and 3/4 3/4 is greater than 3/5 So, 3/5 < 3/4 < 7/8 Distance from least to greatest is 3/5, 3/4 , 7/8 Question 3. Santiago collects 435 cents in nickels. How many nickels does he collect? Options: a. 58 b. 78 c. 85 d. 87 Answer: d. 87 Explanation: As per the given data, Santiago collects 435 cents in nickels 1 nickel worth is 5 cents Then, nickels per 435 cents = 435/5 = 87 So, Santiago collects 87 nickels Question 4. Lisa has three classes that each last 50 minutes. What is the total number of minutes the three classes last? Options: a. 15 minutes b. 150 minutes c. 153 minutes d. 156 minutes Answer: b. 150 minutes Explanation: From the given data, Lisa has three classes that each last 50 minutes The total number of minutes the three classes last = 3×50 =150 minutes Question 5. Some students were asked to write a composite number. Which student did NOT write a composite number? Options: a. Alicia wrote 2. b. Bob wrote 9. c. Arianna wrote 15. d. Daniel wrote 21. Answer: a. Alicia wrote 2. Explanation: As per the information Some students were asked to write a composite number a. Alicia wrote 2 Factors of 2 is 1 and 2 b. Bob wrote 9 Factors of 9 is 1, 3, 9 c. Arianna wrote 15 Factors of 15 is 1, 3, 5, 15 d. Daniel wrote 21 Factors of 21 is 1,3,7,21 So, Alicia did not write a composite number Question 6. Mrs. Carmel serves $$\frac{6}{8}$$ of a loaf of bread with dinner. Which fraction is equivalent to $$\frac{6}{8}$$? Options: a. $$\frac{2}{4}$$ b. $$\frac{9}{16}$$ c. $$\frac{2}{3}$$ d. $$\frac{3}{4}$$ Answer: d. $$\frac{3}{4}$$ Explanation: As per the given information Mrs. Carmel serves 6/8 of a loaf of bread with dinner To find the equivalent fraction of 6/8, simplify the 6/8 by dividing with the 2 (6÷2)/(8÷2) = ¾ So, the equivalent fraction of 6/8 is 3/4 ### Page No. 377 Question 1. For numbers 1a–1d, tell whether the fractions are equivalent by selecting the correct symbol. a. $$\frac{4}{16}$$ _____ $$\frac{1}{4}$$ Answer: $$\frac{4}{16}$$ = $$\frac{1}{4}$$ Explanation: 4/16 and 1/4 Divide the numerator and denominator of 4/16 with 4 (4÷4)/(16÷4) = 1/4 So, 4/16 = 1/4 Question 1. b. $$\frac{3}{5}$$ _____ $$\frac{12}{15}$$ Answer: $$\frac{3}{5}$$ ≠ $$\frac{12}{15}$$ Explanation: 3/5 and 12/15 Multiply the numerator and denominator of 3/5 with 3 (3×3)/(5×3) = 9/15 So, 3/5 ≠ 12/15 Question 1. c. $$\frac{5}{6}$$ _____ $$\frac{25}{30}$$ Answer: $$\frac{5}{6}$$ = $$\frac{25}{30}$$ Explanation: c. 5/6 and 25/30 Multiply the numerator and denominator of 5/6 with 5 (5×5)/(6×5) = 25/30 So, 5/6 = 25/30 Question 1. d. $$\frac{6}{10}$$ _____ $$\frac{5}{8}$$ Answer: $$\frac{6}{10}$$ ≠ $$\frac{5}{8}$$ Explanation: 6/10 and 5/8 Divide the numerator and denominator of 6/10 with 2 (6÷2)/(10÷2) = 3/5 6/10 ≠5/8 Question 2. Juan’s mother gave him a recipe for trail mix. $$\frac{3}{4}$$ cup cereal $$\frac{2}{3}$$ cup almonds $$\frac{1}{4}$$ cup peanuts $$\frac{1}{2}$$ cup raisins Order the ingredients used in the recipe from least to greatest. Type below: _________ Answer: As per the given data, Juan’s mother gave him a recipe for trail mix 3/4 cup cereal and 2/3 cup almonds 1/4 cup peanuts and 1/2 cup raisins 3/4 is closer to 1 2/3 is greater than 1/2 1/4 is less than 1/2 1/2 is equal to 1/2 So, 1/4 < 1/2 <2/3 < 3/4 So, Jaun’s mother gave him a recipe for trail mix in order 1/4 cup of peanuts < 1/2 cup of raisins < 2/3 cup almonds < 3/4 cup of cereals Question 3. Taylor cuts $$\frac{1}{5}$$ sheet of construction paper for an arts and crafts project. Write $$\frac{1}{5}$$ as an equivalent fraction with the denominators shown. Type below: _________ Answer: From the given data, Taylor cuts 1/5 sheet of construction paper for an arts and crafts project So, the equivalent fractions of 1/5 Multiply the numerator and denominator of 1/5 with 2 (1×2)/(5×2) = 2/10 Multiply the numerator and denominator of 1/5 with 3 (1×3)/(5×3) = 3/15 Multiply the numerator and denominator of 1/5 with 5 (1×5)/(5×5) = 5/25 Multiply the numerator and denominator of 1/5 with 8 (1×8)/(5×8) = 8/40 So, the equivalent fractions of 1/5 are 2/10, 3/15, 5/25, 8/40 Question 4. A mechanic has sockets with the sizes shown below. Write each fraction in the correct box. $$\frac{7}{8} in. \frac{3}{16} in. \frac{1}{4} in. \frac{3}{8} in. \frac{4}{8} in. \frac{11}{16} in.$$ Type below: _________ Answer: Explanation: As per the given data, A mechanic has sockets with the sizes 7/8 inch, 3/16 inch, 1/4 inch, 3/8 inch, 4/8 inch, 11/16 inch 7/8 is greater than 1/2 3/16 is less than 1/2 1/4 is less than 1/2 3/8 is less than 1/2 4/8 is equal to 1/2 11/16 is greater than 1/2 ### Page No. 378 Question 5. Darcy bought $$\frac{1}{2}$$ pound of cheese and $$\frac{3}{4}$$ pound of hamburger for a barbecue. Use the numbers to compare the amounts of cheese and hamburger Darcy bought. Answer: Explanation: From the given data, Darcy bought 1/2 pound of cheese and 3/4 pound of hamburger for a barbecue 3/4 is greater than 1/2 Question 6. Brad is practicing the piano. He spends $$\frac{1}{4}$$ hour practicing scales and $$\frac{1}{3}$$ hour practicing the song for his recital. For numbers 6a–6c, select Yes or No to tell whether each of the following is a true statement. a. 12 is a common denominator of $$\frac{1}{4}$$ and $$\frac{1}{3}$$. i. yes ii. no Answer: i. yes Explanation: 12 is a common denominator of 1/3 and 1/4 Question 6. b. The amount of time spent practicing scales can be rewritten as $$\frac{3}{12}$$. i. yes ii. no Answer: i. yes Explanation: b. The amount of time spent practicing scales can be rewritten as 3/12 Multiply the numerator and denominator of 1/4 with 3 (1×3)/(4×3) = 3/12 Yes, amount of time spent practicing scales can be rewritten as 3/12 Question 6. c. The amount of time spent practicing the song for the recital can be rewritten as $$\frac{6}{12}$$. i. yes ii. no Answer: ii. no Explanation: c. The amount of time spent practicing the song for the recital can be rewritten as 6/12 The amount of time spent practicing for the song for his recital = 1/3 Multiply the numerator and denominator of 1/3 with 4 (1×4)/(3×4) = 4/12 No, time spent practicing the song for the recital can not be written as 6/12 Question 8. Which pairs of fractions are equivalent? Mark all that apply. a. $$\frac{8}{12} \text { and } \frac{2}{3}$$ b. $$\frac{3}{4} \text { and } \frac{20}{24}$$ c. $$\frac{4}{5} \text { and } \frac{12}{16}$$ d. $$\frac{7}{10} \text { and } \frac{21}{30}$$ Answer: a. $$\frac{8}{12} \text { and } \frac{2}{3}$$ Explanation: a. 8/12 and 2/3 Multiply the numerator and denominator of 2/3 with 4 (2×4)/(3×4) = 8/12 So, 8/12 = 2/3 b. 3/4 and 20/24 Multiply the numerator and denominator of 3/4 with 6 (3×6)/(4×6) = 18/24 c. 4/5 and 12/16 4/5 ≠ 12/16 d. 7/10 and 21/30 Multiply the numerator and denominator of 7/10 with 3 (7×3)/(10×3) =21/30 So, 7/10 = 21/30 Question 9. Sam worked on his science fair project for $$\frac{1}{4}$$ hour on Friday and $$\frac{1}{2}$$ hour on Saturday. What are four common denominators for the fractions? Explain your reasoning. Answer: From the given data, Sam worked on his science fair project for 1/4 hour on Friday and 1/2 hour on Saturday 4,8,12,16 are all common denominators because they all multiples of 2 and 4 ### Page No. 379 Question 10. Morita works in a florist shop and makes flower arrangements. She puts 10 flowers in each vase, and $$\frac{2}{10}$$ of the flowers are daisies. Part A If Morita makes 4 arrangements, how many daisies does she need? Show how you can check your answer. _____ daisies Answer: 8 daisies Explanation: If Morita makes 4 arrangements, 4 X 2 = 8. Question 10. Part B Last weekend, Morita used 10 daisies to make flower arrangements. How many flowers other than daisies did she use to make the arrangements? Explain your reasoning. _____ other flowers Answer: 40 other flowers Explanation: If she used 10 daises, she must have made 5 arrangements. In each vase, she put $$\frac{2}{10}$$ of the flowers are daisies. So, remaining flowers for each vase = 10 – 2 = 8. If she made 5 arrangements, 8 X 5 = 40 other flowers. Question 11. In Mary’s homeroom, $$\frac{10}{28}$$ of the students have a cat, $$\frac{6}{12}$$ have a dog, and $$\frac{2}{14}$$ have a pet bird. For numbers 11a–11c, select True or False for each statement. a. In simplest form, $$\frac{5}{14}$$ of the students have a cat. i. True ii. False Answer: i. True Explanation: In simplest form 5/14 of the students have a cat From the above, 10/28 of the students have a cat Divide the numerator and denominator of 10/28 with 2 (10÷2)/(28÷2) = 5/14 True Question 11. b. In simplest form, $$\frac{2}{4}$$ of the students have a dog. i. True ii. False Answer: i. True Explanation: In simplest form, 2/4 of the students have a dog From the above, 6/12 of the students have a dog Divide the 6/12 with 3 (6 = 2/4 True Question 11. c. In simplest form, $$\frac{1}{7}$$ of the students have a pet bird. i. True ii. False Answer: i. True Explanation: In the simplest form, 1/7 of the students have a pet bird From the data, 2/14 of the students have a pet bird Divide the numerator and denominator of 2/14 with 2 (2÷2)/(14÷2) = 1/7 True ### Page No. 380 Question 12. Regina, Courtney, and Ellen hiked around Bear Pond. Regina hiked $$\frac{7}{10}$$ of the distance in an hour. Courtney hiked $$\frac{3}{6}$$ of the distance in an hour. Ellen hiked 38 of the distance in an hour. Compare the distances hiked by each person by matching the statements to the correct symbol. Each symbol may be used more than once or not at all. Type below: _________ Answer: Explanation: From the given information Regina, Courtney, and Ellen hiked around Bear Pond Regina hiked 7/10 of the distance in an hour Courtney hiked 3/6 of the distance in an hour Ellen hiked 3 /8 of the distance in an hour Compare 7/10 and 3/6 The common denominator of 7/10 and 3/6 is 30 (7×3)/(10×3) and (3×5)/(6×5) 21/30 and 15/30 So, 21/30 > 15/30 So, 7/10 > 15/30 Compare 3/8 and 3/6 The common denominator of 3/8 and 3/6 is 24 (3×3)/(8×3) and (3×4)/(6×4) 9/24 and 12/24 = 9/24 < 12/24 = 3/8 < 3/6 Compare 7/10 and 3/8 The common denominator of 7/10 and 3/8 is 40 (7×4)/(10×4) and (3×5)/(8×5) 28/40 >15/40 = 7/10 > 3/8 Question 13. Ramon is having some friends over after a baseball game. Ramon’s job is to make a vegetable dip. The ingredients for the recipe are given. Part A Which ingredient does Ramon use the greater amount of, buttermilk or cream cheese? Explain how you found your answer. Type below: _________ Answer: Ramon use 5/8 cup of buttermilk and 1/2 cup cream cheese By comparing these two ingredients The common denominator of 5/8 and 1/2 are 8 (1×4)/(2×4) =4/8 So, 5/8 > 4/8 So, 5/8 cup buttermilk is > ½ cup cream cheese Question 13. Part B Ramon says that he needs the same amount of two different ingredients. Is he correct? Support your answer with information from the problem. ______ Answer: Ramon says that he needs the same amount of two ingredients Yes, Ramon uses 3/4 cup parsley and 6/8 cup scallions Multiply the 3/4 with 2 (3×2)/(4×2) = 6/8 So, Ramon uses the same amount that is 3/4 cup for parsley and scallions ### Page No. 381 Question 14. Sandy is ordering bread rolls for her party. She wants $$\frac{3}{5}$$ of the rolls to be whole wheat. What other fractions can represent the part of the rolls that will be whole wheat? Shade the models to show your work. Type below: _________ Answer: Explanation: As per the information, Sandy is ordering bread rolls for her party She wants 3/5 of the rolls to be whole wheat For an equivalent fraction of 3/5, multiply with 5 (3×5)/(5×5) = 15/25 Again multiply the 15/25 with 4 (15×4)/(25×4) = 60/100 Question 15. Angel has $$\frac{4}{8}$$ yard of ribbon and Lynn has $$\frac{3}{4}$$ yard of ribbon. Do Angel and Lynn have the same amount of ribbon? Shade the model to show how you found your answer. Explain your reasoning. Type below: _________ Answer: Angel and Lynn didn’t have the same amount of ribbon. 4/8 is a greater fraction compared to 3/4. So, Angel’s ribbon is long compared to Lynn’s ribbon. Question 16. Ella used $$\frac{1}{4}$$ yard of red ribbon. Fill in each box with a number from the list to show equivalent fractions for $$\frac{1}{4}$$. Not all numbers will be used. Type below: _________ Answer: Explanation: 1/4 = 2/8 = 4/16 = 3/12 ### Page No. 382 Question 17. Frank has two same-size rectangles divided into the same number of equal parts. One rectangle has $$\frac{3}{4}$$ of the parts shaded, and the other has $$\frac{1}{3}$$ of the parts shaded. Part A Into how many parts could each rectangle be divided? Show your work by drawing the parts of each rectangle. _____ parts Answer: 12 parts Question 17. Part B Is there more than one possible answer to Part A? If so, did you find the least number of parts into which both rectangles could be divided? Explain your reasoning. Type below: _________ Answer: Yes, as long it is a multiple of 12. And yes,12 is the least in order to have 1 rectangle have 3/4 shaded and the other 1/3 shaded. Question 18. Suki rode her bike $$\frac{4}{5}$$ mile. Claire rode her bike $$\frac{1}{3}$$ mile. They want to compare how far they each rode their bikes using the benchmark $$\frac{1}{2}$$. For numbers 18a–18c, select the correct answers to describe how to solve the problem. a. Compare Suki’s distance to the benchmark: $$\frac{4}{5}$$ _____ $$\frac{1}{2}$$ Answer: $$\frac{4}{5}$$ ≠ $$\frac{1}{2}$$ Explanation: The fraction $$\frac{4}{5}$$ is not equal to $$\frac{1}{2}$$. Question 18. b. Compare Claire’s distance to the benchmark: $$\frac{1}{3}$$ _____ $$\frac{1}{2}$$ Answer: $$\frac{1}{3}$$ ≠ $$\frac{1}{2}$$ Explanation: The fraction $$\frac{1}{3}$$ is not equal to $$\frac{1}{2}$$ Question 18. c. Suki rode her bike _____ Claire. Answer: Suki rode her bike faster than Claire. ### Page No. 387 Use the model to write an equation. Question 1. Type below: _________ Answer: $$\frac{3}{5}$$ + $$\frac{1}{5}$$ = $$\frac{4}{5}$$ Question 2. Type below: _________ Answer: $$\frac{2}{3}$$ – $$\frac{1}{3}$$ = $$\frac{1}{3}$$ Question 3. Type below: _________ Answer: $$\frac{1}{4}$$ + $$\frac{1}{4}$$ = $$\frac{2}{4}$$ Question 4. Type below: _________ Answer: 1 – $$\frac{5}{8}$$ = $$\frac{8}{8}$$ – $$\frac{5}{8}$$ = $$\frac{3}{8}$$ Use the model to solve the equation. Question 5. $$\frac{3}{4}-\frac{1}{4}$$ = $$\frac{□}{□}$$ Answer: $$\frac{2}{4}$$ Question 6. $$\frac{5}{6}+\frac{1}{6}$$ = $$\frac{□}{□}$$ Answer: $$\frac{6}{6}$$ = 1 Question 7. Reason Abstractly Sean has $$\frac{1}{5}$$ of a cupcake and $$\frac{1}{5}$$ of a large cake. a. Are the wholes the same? Explain. ______ Answer: Yes; From the given information, the fraction of the cupcake and large cake are the same. Explanation: Question 7. Does the sum $$\frac{1}{5}+\frac{1}{5}=\frac{2}{5}$$ make sense in this situation? Explain. ______ Answer: Yes; it makes sense. From the given data, 1 part is out of 5 parts. So, adding two fractions (1 part is out of 5 parts), the complete fraction becomes 2/5. Question 8. Carrie’s dance class learned $$\frac{1}{5}$$ of a new dance on Monday, and $$\frac{2}{5}$$ of the dance on Tuesday. What fraction of the dance is left for the class to learn on Wednesday? $$\frac{□}{□}$$ Answer: $$\frac{3}{5}$$ Explanation: The fraction of left for the class to learn on Wednesday is $$\frac{3}{5}$$. ### Page No. 388 Question 9. Samantha and Kim used different models to help find $$\frac{1}{3}+\frac{1}{6}$$. Whose model makes sense? Whose model is nonsense? Explain your reasoning below each model. Answer: Both Samantha and Kim’s statements make sense. Because both models have an equal number of fractions for each diagram. Question 10. Draw a model you could use to add $$\frac{1}{4}+\frac{1}{2}$$. Type below: ___________ Answer: Question 11. Cindy has two jars of paint. One jar is $$\frac{3}{8}$$ full. The other jar is $$\frac{2}{8}$$ full. Use the fractions to write an equation that shows the amount of paint Cindy has. Type below: ___________ Answer: $$\frac{3}{8}+\frac{2}{8}$$ = $$\frac{5}{8}$$ ### Conclusion: By downloading the Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison PDF, students of grade 4 will aid you to understand different topics in Chapter 6 easily. Prepare well with the help of Go Math Grade 4 Answer Key PDFand solve each and every question properly. For more help utilize this Go Math Grade 4 Solution Key Chapter 6 Fraction Equivalence and Comparison PDF and gain what you require. ## Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Go Math Grade 4 Answer Key Chapter 5 includes topics like Factors, Common factors, Divisibilities and Review tests, etc. that aid students to solve the homework and assessment tests. Also, it is the best and ultimate guide for exam preparation. You will find every question was explained in a simplistic way so that you are able to understand the concepts easily. Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns pdf links are available here for each and every lesson. So, kickstart your preparation and score good grades in the exams. ## Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Improve your Problem-Solving Skills utilizing the Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns. Start practicing the question covered in the Go Math 4th grade Solution Key and Cross Check the Solutions of Chapter 5 Factors, Multiples, and Patterns from here. So that you can easily rectify your mistakes and fill up the knowledge gap. Take the help from the direct links available below and solve the problems covered in Go Math Grade 4 Answer Key. ### Lesson 1: Model Factors ### Lesson 2: Factors and Divisibility ### Lesson 3: Problem Solving • Common Factors ### Lesson 4: Factors and Multiples ### Lesson 5: Prime and Composite Numbers ### Lesson 6: Algebra • Number Patterns ### Chapter 5 Review/Test ### Common Core – Model Factors – Page No. 283 Model Factors Use tiles to find all the factors of the product. Record the arrays on grid paper and write the factors shown. Question 1. Question 2. Write the factors of: 30 Answer: The Factors Of 30 are: 1,2,3,5,6,10,15,30. Explanation: Factors are the numbers which divides the original number completely. Here, we can see the numbers which gives the result as 30 when multiplied together.So the factors of 30 are 1,2,3.5,6,10,15,30. 1×30=30 2×15=30 3×10=30 5×6=30 6×5=30 10×3=30 15×2=30 30×1=30 Question 3. Write the factors of: 45 Answer: The Factors Of 45 are:1,3,5,9,15,45. Explanation: Factors are the numbers which divides the original number completely. Here, we can see the numbers which gives the result as 45 when multiplied together.So the factors of 45 are:1,3,5,9,15,45. 1×45=45 3×15=45 5×9=45 9×5=45 15×3=45 45×1=45 Question 4. Write the factors of: 19 Answer: The Factors Of 19 are:1,19. Explanation: Since 19 is a Prime number that means it is divisible by 1 and itself. So the factors of 19 are 1,19. 1×19=19 19×1=19. Question 7. Write the factors of 22 Answer: The Factors Of 22 are:1,2,11,22. Explanation: Factors are the numbers which divides the original number completely. The factors of 22 are:1,2,11,22. 1×22=22 2×11=22 11×2=22 22×1=22. Question 8. Write the factors of: 4 Answer: The Factors Of 4 are:1,2,4. Explanation: Factors are the numbers which divides the original number completely. The Factors Of 4 are:1,2,4. 1×4=4 2×2=4 4×1=4. Question 9. Write the factors of: 26 Answer: The Factors Of 26 are:1,2,13,26. Explanation: Factors are the numbers which divides the original number completely. Here, we can see the numbers which gives the result as 26 when multiplied together.So the factors of 26 are:1,2,13,26. 1×26=26 2×13=26 13×2=26 26×1=26. Question 10. Write the factors of: 49 Answer: The Factors Of 49 are:1,7,49. Explanation: Factors are the numbers which divides the original number completely. The Factors Of 49 are:1,7,49. 1×49=49 7×7=49 49×1=49. Question 14. Eduardo thinks of a number between 1 and 20 that has exactly 5 factors. What number is he thinking of? Answer: 16 Explanation: If find factors for 1 to 20 we don’t get exactly 5 factors for any number except 16. So the answer is 16. ### Common Core – Factors – Page No. 284 Lesson Check Question 1. Which of the following lists all the factors of 24? Options: a. 1, 4, 6, 24 b. 1, 3, 8, 24 c. 3, 4, 6, 8 d. 1, 2, 3, 4, 6, 8, 12, 24 Answer: d(1, 2, 3, 4, 6, 8, 12, 24) Explanation:Factors are the numbers which divides the original number completely. Here, we can see the numbers which gives the result as 24 when multiplied together.So the factors of 24 are:1, 2, 3, 4, 6, 8, 12, 24. 1×24=24 2×12=24 3×8=24 4×6=24 6×4=4 8×3=24 12×2=24 24×1=24 Question 2. Natalia has 48 tiles. Which of the following shows a factor pair for the number 48? Options: a. 4 and 8 b. 6 and 8 c. 2 and 12 d. 3 and 24 Answer: b(6 and 8) Explanation: 6 and 8 are factor pair for 48 because 6×8=48. Spiral Review Question 3. The Pumpkin Patch is open every day. If it sells 2,750 pounds of pumpkins each day, about how many pounds does it sell in 7 days? Options: a. 210 pounds b. 2,100 pounds c. 14,000 pounds d. 21,000 pounds Answer: d Explanation: Let’s round off 2750 pounds to 3000 pounds. In one day 3000 pounds pumpkins were sold out, and in 7 days?? —- 3000×7= 21,000 pounds. Question 4. What is the remainder in the division problem modeled below? Options: a. 2 b. 3 c. 5 d. 17 Answer: a Explanation: We can see in the above figure 3 circles with 5 sub circles inside it and a pair of sub circles. Here total sub circles are (3×5)+2=17. If we divide 17 with 3 then we will get reminder as 2. So answer is 2. Question 5. Which number sentence is represented by the following array? Options: a. 4 × 5 = 20 b. 4 × 4 = 16 c. 5 × 2 = 10 d. 5 × 5 = 25 Answer: a Explanation: As we can see 4 rows and 5 squares, So 4 × 5 = 20. Question 6. Channing jogs 10 miles a week. How many miles will she jog in 52 weeks? Options: a. 30 miles b. 120 miles c. 200 miles d. 520 miles Answer: d Explanation: No.of weeks = 52. So 1 week = 10 miles, then 52 weeks =????? 52×10=520 miles. ### Page No. 287 Question 1. Is 4 a factor of 28? Draw a model to help. Think: Can you make a rectangle with 28 squares in 4 equal rows? 4 ______ a factor of 28. Type below: __________ Is 5 a factor of the number? Write yes or no. Question 2. 27 Answer: No. Explanation: Factors of 27 are 1,3,9,27. So the answer is No. Question 3. 30 Answer : Yes. Explanation: As the last digit is 0 which is divisible 5. Question 4. 36 Answer: No Explanation: 36 is not divisible by 5, So the answer is no Question 5. 53 Answer: No Explanation: Factors of 53 are 1, 53. So the answer is No. Is 9 a factor of the number? Write yes or no. Question 6. 54 Answer: Yes. Explanation: As 54 is divisible by 9. Question 7. 63 Answer: Yes. Explanation: 63 is divisible by 9, So the answer is Yes Question 8. 67 Answer: No. Explanation: 67 is a prime number which means it is divisible by 1 and itself. So the answer is No. Question 9. 93 Answer: No. Explanation: The factors of 93 are 1,3,31 and 93. So the answer is No. List all the factor pairs in the table. Question 10. Answer: 1×24=24 1,24 2×12=24 2,12 3×8=24 3,8 4×6=24 4,6 Explanation: Factors of 24. Question 11. Answer: 1×39=39 1,39 3×13=39. 3,13 Explanation: Factors of 39. Practice: Copy and Solve List all the factor pairs for the number. Make a table to help. Question 12. 56 Answer: 1×56=56 1,56 2×23=56 2,23 4×14=56 4,14 7×8=56 7,8 8×7=56 8,7 Explanation: Factors of 56. Question 13. 64 Answer: 1×64=64 1,64 2×32=64 2,32 4×16=64 4,16 8×8=64 8,8 Explanation: Factors of 64 and factor pair for 64 is 8,8. ### Page No. 288 Use the table to solve 14–15. Question 14. Dirk bought a set of stamps. The number of stamps in the set he bought is divisible by 2, 3, 5, 6, and 9. Which set is it? Answer: 90 Explanation: 90 is divisible by all numbers 2,3,5,6, and 9. So the answer is 90. Question 15. Geri wants to put 6 stamps on some pages in her stamp book and 9 stamps on other pages. Explain how she could do this with the stamp set for Sweden. Answer: 10 pages with 6 stamps and 2 pages with 9 stamps. Explanation: Geri could break 78 into 60+18, As 60 is divisible by 6, and 18 is divisible by 9. Then she could make 10 pages with 6 stamps as 60÷6=10 and 2 pages with 9 stamps as 18÷9=2. Question 16. Use Counterexamples George said if 2 and 4 are factors of a number, then 8 is a factor of the number. Is he correct? Explain. Answer: No Explanation: Because if we 12 as an example, 2 and 4 are factors of 12 but not 8. Question 17. Classify the numbers. Some numbers may belong in more than one box. Answer: Divisible by 5 and 9 — 45 Divisible by 3 and 9 — 27,45,54,72,81 Divisible by 2 and 6 — 54,72,84. ### Common Core – Factors and Divisibility – Page No. 289 Is 6 a factor of the number? Write yes or no. Question 1. Question 2. 56 Answer: No Explanation: 56 is not divisible by 6. So the answer is No. Question 3. 42 Answer: Yes Explanation: Since 42 is divisible by 6. Question 4. 66 Answer: Yes Explanation: 66 is divisible by 6. Is 5 a factor of the number? Write yes or no. Question 7. 60 Answer: Yes Explanation: 60 is a factor of 5 because 60 is divisible by 5. Question 8. 39 Answer: No Explanation: As 39 is not divisible by 5. So the answer is No. List all the factor pairs Question 11. List all the factor pairs for 48. Answer: Factor pairs of 48 are (1,48),(2,24),(3,16),(4,12),(6,8),(12,2),(6,3),(24,2),(48,1). Explanation: Factor pairs are the pairs when we multiplied both numbers will get the result. Here factor pairs for 48 are 1×48=48 (1,48) 2×24=48 (2,24) 3×16=48 (3,16) 4×12=48 (4,12) 6×8 =48 (6,8) Problem Solving Question 12. Bryson buys a bag of 64 plastic miniature dinosaurs. Could he distribute them equally into six storage containers and not have any left over? Answer: No Explanation: 64 is not divisible by 6, So he cannot distribute them equally into six storage containers. Question 13. Lori wants to distribute 35 peaches equally into baskets. She will use more than 1 but fewer than 10 baskets. How many baskets does Lori need? Answer: 5 or 7. Explanation: First we need to know the factors of 35. The factors of 35 are 1,5,7,35. As Lori uses more than 1 but fewer than 10, the answer is 5 or 7. Lori can distribute 35 peaches equally in 5 or 7 baskets. ### Common Core – Factors – Page No. 290 Lesson Check Question 1. Which of the following numbers has 9 as a factor? Options: a. 28 b. 30 c. 39 d. 45 Answer: d Explanation: 45 is divisible 9. So the answer is 45. Question 2. Which of the following numbers does NOT have 5 as a factor? Options: a. 15 b. 28 c. 30 d. 45 Answer: 28 Explanation: 28 is not divisible by 5. So 28 is not a factor of 5. Spiral Review Question 3. Which of the following shows a strategy to use to find 4 × 275? Options: a. (4 × 300) + (4 × 25) b. (4 × 300) – (4 × 25) c. (4 × 275) – 100 d. (4 × 200) + 75 Answer: b Explanation: First we must replace 300-25 in the place of 275 then it becomes 4×(300-25), Now we must use the distributive property of multiplication then (4×300)-(4×25). So the answer is b. Question 4. Jack broke apart 5 × 216 as (5 × 200) + (5 × 16) to multiply mentally. What strategy did Jack use? Options: a. the Commutative Property b. the Associative Property c. halving and doubling d. the Distributive Property Answer: d Explanation: Distributive property means if we multiply a sum by a number is same as multiplying each addend by the number and adding the products. This is the strategy Jack used. Question 5. Jordan has$55. She earns $67 by doing chores. How much money does Jordan have now? Options: a.$122
b. $130 c.$112
d. $12 Answer: a Explanation: Jordan has$55, she earns by doing chores is $67. So total money is$55+$67=$122.

Question 6.
Trina has 72 collector’s stamps. She puts 43 of the stamps into a stamp book. How many stamps are left?
Options:
a. 29
b. 31
c. 39
d. 115

Explanation: Stamps left are 72-43=29.

### Page No. 293

Question 1.
Lucy has 40 bean plants, 32 tomato plants, and 16 pepper plants. She wants to put the plants in rows with only one type of plant in each row. All rows will have the same number of plants. How many plants can Lucy put in each row?
First, read the problem and think about what you need to find. What information will you use? How will you use the information?

Answer: We will find common factors for 40,32 and 16.

Question 1.
Next, make a list. Find the factors for each number in the problem.

Factors of 40 are — 1,2,4,5,8,10,20,40
Factors of 32 are — 1,2,4,8,16,32
Factors of 16 are — 1,2,4,8,16

Question 1.
Finally, use the list. Circle the common factors.
So, Lucy can put ___ , ___ , ___ , or ___ plants in each row.

Explanation: Because 1,2,4,8, are common factors in 40,32,16.

Question 2.
What if Lucy has 64 bean plants instead of 40 bean plants? How many plants can Lucy put in each row?

Explanation: Here we need to find the factors of 64,32 and 16. We get common factors as 1,2,4,8,16.

### Page No. 294

Question 5.
Analyze A number is called a perfect number if it equals the sum of all of its factors except itself. For instance, 6 is a perfect number because its factors are 1, 2, 3, and 6, and 1 + 2 + 3 = 6. What is the next greater perfect number?

Explanation: The factors of 28 are 1,2,4,7,14 and 28. If we add 1+2+4+7+14 we will get 28. So 28 is a perfect number.

Question 6.
Sona knits 10 squares a day for 7 days. Can she sew together the squares to make 5 equal-sized blankets? Explain.

Explanation: As 10×7= 70 which is a factor of 5.

Question 7.
Julianne earned $296 working at a grocery store last week. She earns$8 per hour. How many hours did Julianne work?

Explanation: Julianne earned $296 in last week. Per hour she earns$8, So total no.of hours did she worked is
296÷8= 37 hours.

Question 8.
There are 266 students watching a play in the auditorium. There are 10 rows with 20 students in each row and 5 rows with 8 students in each row. How many students are sitting in each of the 2 remaining rows if each of those rows has an equal number of students?

Explanation: Total number of students is 266. In which 10 rows were filled with 20 students which means 10×20=200 students, and 5 rows were filled with 8 students which means 5×8= 40 students. The total students filled are 240. And to know how many students filled in the remaining 2 rows we need to subtract 266-240=26, As students are filled in 2 rows 26÷2= 13.

Question 9.
Ben is planting a garden with 36 zinnias, 18 marigolds, and 24 petunias. Each row will have only one type of plant. Ben says he can put 9 plants in each row. He listed the common factors of 36, 18 and 24 below to support his reasoning.
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
18: 1, 2, 3, 6, 8, 9, 18
24: 1, 2, 3, 4, 6, 8, 9, 12, 24
Is he correct? Explain your answer. If his reasoning is incorrect, explain how he should have found the answer.

Explanation: The factors of 18 and 24 are incorrect which he listed. And the common factors for 36,24 and 18 are 1,2,3 and 6. So he can put 1,2,3 and 6 plants in a row.

### Common Core – Common Factors – Page No. 295

Problem Solving Common Factors

Solve each problem.

Question 1.
Grace is preparing grab bags for her store’s open house. She has 24 candles, 16 pens, and 40 figurines. Each grab bag will have the same number of items, and all the items in a bag will be the same. How many items can Grace put in each bag?

Question 2.
Simon is making wreaths to sell. He has 60 bows, 36 silk roses, and 48 silk carnations. He wants to put the same number of items on each wreath. All the items on a wreath will be the same type. How many items can Simon put on each wreath?

Answer:1,2,3,4,6 or 12 items Simon puts on each wreath.

Explanation: First we will find the common factors of 36,48,60
factors of 36 are: 1,2,3,4,6,9,12,18,36.
factors of 48 are: 1,2,3,4,6,8,12,16,24,48
factors of 60 are: 1,2,3,4,5,6,10,12,15,20,30,60.
The common factors of 36,48,60 are 1,2,3,4,6,12. So Simon can put 1,2,3,4,6 or 12 items on each wreath.

Question 5.
A debate competition has participants from three different schools: 15 from James Elementary, 18 from George Washington School, and 12 from the MLK Jr. Academy. All teams must have the same number of students. Each team can have only students from the same school. How many students can be on each team?

Explanation: Lets find the common factors of 12,15,18
factors of 12 are: 1,2,3,4,6,12
factors of 15 are: 1,3,5,15
factors of 18 are: 1,2,3,6,9,18
3 is the common factor for 12,15,18

### Common Core – Common Factors – Page No. 296

Lesson Check

Question 1.
What are all the common factors of 24, 64, and 88?
Options:
a. 1 and 4
b. 1, 4, and 8
c. 1, 4, 8, and 12
d. 1, 4, 8, and 44

Explanation:
factors of 24 are: 1,2,3,4,8,12,24
factors of 64 are: 1,2,4,8,16,32,64
factors of 88 are: 1,2,4,8,11,22,44,88

Question 2.
Which number is NOT a common factor of 15, 45, and 90?
Options:
a. 3
b. 5
c. 10
d. 15

Explanation: As 15 and 45 are not divisible by 10.

Spiral Review

Question 3.
Dan puts $11 of his allowance in his savings account every week. How much money will he have after 15 weeks? Options: a.$165
b. $132 c.$110
d. $26 Answer: a Explanation: Dan puts$11 in his savings account every week, So after 15 weeks it will be 15×11=165.
The total money he will have after 15 weeks is $165. Question 4. James is reading a book that is 1,400 pages. He will read the same number of pages each day. If he reads the book in 7 days, how many pages will he read each day? Options: a. 20 b. 50 c. 140 d. 200 Answer: d Explanation: Total no.of.pages is 1400, no.of pages James read each day is 1400÷7= 200 Question 5. Emma volunteered at an animal shelter for a total of 119 hours over 6 weeks. Which is the best estimate of the number of hours she volunteered each week? Options: a. 10 hours b. 20 hours c. 120 hours d. 714 hours Answer: b Explanation: Total hours Emma volunteered is 119 hours over 6 weeks, how much she volunteered each week is 119÷6= 19.833 i.e 20 hours. We must round off to the nearest one i.e 20 hours. Question 6. Which strategy can be used to multiply 6 × 198 mentally? Options: a. 6 × 198 = (6 × 19) + (6 × 8) b. 6 × 198 = (6 × 200) + (6 × 2) c. 6 × 198 = (6 × 200) – (6 × 2) d. 6 × 198 = (6 + 200) × (6 + 2) Answer: c Explanation: By Distributive property of multiplication 6×198 can be written as (6 × 200) – (6 × 2). ### Page No. 297 Choose the best term from the box. Question 1. A number that is multiplied by another number to find a product is called a Answer: Factor. Question 2. A number is _________ by another number if the quotient is a counting number and the remainder is zero. Answer: Divisible. List all the factors from least to greatest. Question 3. 8 Answer: 1,2,4,8 Question 4. 14 Answer: 1,2,7,14 Is 6 a factor of the number? Write yes or no. Question 5. 81 Answer: No Explanation: 81 is not divisible by 6 Question 6. 45 Answer: No Explanation: 45 is not divisible by 6 Question 7. 42 Answer: Yes Explanation: 42 is divisible by 6 Question 8. 56 Answer: No. Explanation: 56 is not divisible by 6 List all the factor pairs in the table. Question 9. Answer: 1×64=64 1,64 2×32=64 2,32 4×16=64 4,16 8×8=64 8,8 Explanation: Factors of 64 Question 10. Answer: 1×44=44 1,44 2×22=44 2,22 11×4=44 11,4 List the common factors of the numbers. Question 11. 9 and 18 Answer: 1,3,9 Explanation: Factors of 9 are: 1,3,9 Factors of 18 are: 1,2,3,9,18 Question 12. 20 and 50 Answer: 1,2,5,10 Explanation: Factors of 20 are: 1,2,4,5,10,20 Factors of 50 are: 1,2,5,10,25,50 ### Page No. 298 Question 15. Sandy has 16 roses, 8 daisies, and 32 tulips. She wants to arrange all the flowers in the bouquets. Each bouquet has the same number of flowers and the same type of flower. What is the greatest number of flowers that could be in a bouquet? Answer: 2 roses, 1 daisy, and 4 tulips in 8 bouquets. Explanation: First we must add all the flowers i.e 16+8+32= 56, Now we can divide 56 flowers equally in each bouquet. Like 2 roses, 1 daisy and 4 tulips in 8 bouquets or 8 roses in 2 bouquets, 8 daisies in 1 bouquet, and 8 tulips in 4 bouquets. Question 16. Amir arranged 9 photos on a bulletin board. He put the photos in rows. Each row contains the same number of photos. How many photos could be in each row? Answer: 9 photos in a row and 3 photos in 3 rows, or 9 in 1 row. Explanation: Factors of 9 are 1,3,9. So Amir can arrange 9 photos in a row and 3 photos in 3 rows, or 9 in 1 row. ### Page No. 301 Question 1. Multiply to list the next five multiples of 4. 4 , _____ , _____ , _____ , _____ , _____ 1 × 4 4 , _____ , _____ , _____ , _____ , _____ Answer: 4 1×4 8 2×4 12 3×4 16 4×4 20 4×5 Explanation: Multiplies of 4 Is the number a factor of 6? Write yes or no. Question 2. 2 Answer: Yes Explanation: 6 is divisible by 2. So 2 is the factor of 6. Question 3. 6 Answer: Yes Explanation: 6 is divisible by 6. Question 4. 16 Answer: No Explanation: 16 is not divisible by 6 Question 5. 18 Answer: Yes Explanation: 18 is divisible by 6 Is the number a multiple of 6? Write yes or no. Question 6. 3 Answer: No Explanation: Multiples of 6 are 6,12,18,24,30, etc. Question 7. 6 Answer: Yes Explanation: 1×6= 6. So 6 is multiple of 6. Question 8. 16 Answer: No Explanation: Multiples of 6 are 6,12,18,24,30, etc. Question 9. 18 Answer: Yes Explanation: Multiples of 6 are 6,12,18,24,30, etc. Is the number a multiple of 3? Write yes or no. Question 10. 4 Answer: No Explanation: Multiples of 3 are 3,6,9,12,15,etc. Question 11. 8 Answer: No Explanation: Multiples of 3 are 3,6,9,12,15,etc. Question 12. 24 Answer: Yes Explanation: Multiples of 3 are 3,6,9,12,15,etc. Question 13. 38 Answer: No Explanation: Multiples of 3 are 3,6,9,12,15,18,21,24,27,30,33,36,39,42,etc. Question 14. List the next nine multiples of each number. Find the common multiples. Multiples of 2: 2, _________________ Multiples of 8: 8, _________________ Common multiples: _________________ Answer: 8,16. Explanation: Multiples of 2: 2,4,6,8,10,12,14,16,18,20. Multiples of 8: 8,16,24,32,40,48,56,64,72,80. So common multiples are: 8,16 Generalize Algebra Find the unknown number. Tell whether 20 is a factor or multiple of the number. Write factor, multiple, or neither. Question 17. 10 Answer: Multiple Explanation: 2×10= 20. Question 18. 20 Answer: Factor and multiple Explanation: 1×20= 20 20÷1= 20. Question 19. 30 Answer: Neither Explanation: Factors of 30 are: 1,2,3,5,6,10,15,and 30. Multiples of 30 are: 30,60,90,etc. Write true or false. Explain. Question 20. Every whole number is a multiple of 1. Answer: True. Explanation: For every whole number which is multiplied with 1, the result will be that number. Question 21. Every whole number is a factor of 1. Answer: False Explanation: Not every whole number is a factor of 1. Question 22. Julio wears a blue shirt every 3 days. Larry wears a blue shirt every 4 days. On April 12, both Julio and Larry wore a blue shirt. What is the next date that they will both wear a blue shirt? Answer: April 24 Explanation: As Julio wears a blue shirt every 3 days and another shirt in the remaining 4 days, So 4×3 days= 12 Larry wears a blue shirt every 4 days and another shirt in the remaining 3 days, So 3×4 days= 12 12+12= 24. So the next date will be April 24. ### Page No. 302 Complete the Venn diagram. Then use it to solve 23–25. Question 23. What multiples of 4 are not factors of 48? Answer: 20,28,32,36,40,44. Explanation: Multiples of 4 are 4,8,12,16,20,24,28,32,36,40,44,48. Not a factors of 48 are 20,28,32,36,40,44. Question 24. What factors of 48 are multiples of 4? Answer: 4,8,12,16,24,48. Explanation: Multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,48. Factors of 48 are: 1,2,4,8,12,16,24,48. Question 25. Pose a Problem Look back at Problem 24. Write a similar problem by changing the numbers. Then solve. Answer: Let’s take factors of 64 are multiples of 8? 8,16,32,64. Explanation: Multiples of 8 are: 8,16,24,32,40,48,56,64,72,80 Factors of 64 are: 1,2,4,8,16,32,64 Question 26. Kia paid$10 for two charms. The price of each charm was a multiple of $2. What are the possible prices of the charms? Answer:$2,$8 and$4,$6. Explanation: Since the price was multiple of 2 and Kia paid$10 for two charms, So possible prices are $2+$8=$10 and$4+$6=$10.

Question 27.
Look for Structure The answer is 9, 18, 27, 36, 45. What is the question?

Answer: Write the multiples of 9

Question 28.
How do you know whether a number is a multiple of another number?

Answer: When the number is divisible by the number then that number is multiple of another number.

Explanation: For example, if we take a number i.e 8 which is divisible by 2 and 8 is a multiple of 2.

Question 29.
For numbers 29a–29e, select True or False for each statement.
a. The number 45 is a multiple of 9.
i. True
ii. False

Explanation: As 9×5= 45, So 45 is multiple of 9.

Question 29.
b. The number 4 is a multiple of 16.
i. True
ii. False

Explanation: As 16 is divisible by 4 and not a multiple of 16.
Multiple of 16 are : 16,32,48,64,80.

Question 29.
c. The number 28 is a multiple of 4.
i. True
ii. False

Explanation: 4×7=28.

Question 29.
d. The number 4 is a factor of 28.
i. True
ii. False

Explanation:
Factors of 28 are: 1,2,4,7,14,28.

Question 29.
e. The number 32 is a factor of 8.
i. True
ii. False

Explanation:

### Common Core – Factors and Multiples – Page No. 303

Factors and Multiples
Is the number a multiple of 8? Write yes or no.

Question 1.

Question 2.
8

Explanation: Since 8×1=8, it is a multiple of 8

Question 3.
20

Explanation: 20 is not a multiple of 8

Question 4.
40

Explanation: 8×5=40, So 40 is multiple of 8

List the next nine multiples of each number. Find the common multiples.

Tell whether 24 is a factor or multiple of the number. Write factor, multiple, or neither.

Question 8.
6

Explanation: 6×4=24

Question 9.
36

Explanation: 36 is not a factor or multiple of 24.

Question 10.
48

Explanation: 24×2= 48, So 48 is a factor of 24

Problem Solving

### Common Core – Factors and Multiples – Page No. 304

Lesson Check

Question 1.
Which list shows numbers that are all multiples of 4?
Options:
a. 2, 4, 6, 8
b. 3, 7, 11, 15, 19
c. 4, 14, 24, 34
d. 4, 8, 12, 16

Explanation: Multiples of 4 are 4,8,12,16.

Question 2.
Which of the following numbers is a common multiple of 5 and 9?
Options:
a. 9
b. 14
c. 36
d. 45

Explanation: 5×9= 45

Spiral Review

Question 3.
Jenny has 50 square tiles. She arranges the tiles into a rectangular array of 4 rows. How many tiles will be left over?
Options:
a. 0
b. 1
c. 2
d. 4

Explanation: As Jenny arranges in 4 rows, each row contains 12 tiles. So 12×4= 48. The tiles left are 50-48=2.

Question 4.
Jerome added two numbers. The sum was 83. One of the numbers was 45. What was the other number?
Options:
a. 38
b. 48
c. 42
d. 128

Explanation: The sum of two numbers is 83, in that one number is 45. To find another number we will do subtraction,
i.e 83-45=38.

Question 5.
There are 18 rows of seats in the auditorium. There are 24 seats in each row. How many seats are in the auditorium in all?
Options:
a. 42
b. 108
c. 412
d. 432

Explanation:
No.of rows= 18, each row has 24 seats. So total no.of seats are 18×24= 432.

Question 6.
The population of Riverdale is 6,735. What is the value of the 7 in the number 6,735?
Options:
a. 7
b. 700
c. 735
d. 7,000

Explanation: In 6,735 the 7 is in the Hundreds Place. So the answer is 7.

### Page No. 307

Question 1.
Use the grid to model the factors of 18. Tell whether 18 is prime or composite.

Factors of 18: ____ , ____ , ____ , ____ , ____ , ____
Think: 18 has more than two factors.
So, 18 is _________ .

Explanation: The number which has more than two factors is called composite numbers.
Factors of 18 are: 1,2,3,6,9,18.

Tell whether the number is prime or composite.

Question 2.
11
Think: Does 11 have other factors besides 1 and itself?

Explanation: A Prime number is a number that is divisible 1 and itself.

Question 3.
73

Explanation: A Prime number is a number that is divisible 1 and itself.

Question 4.
69

Explanation: The number which has more than two factors is called composite numbers.
Factors of 69 are: 1,3,23,69.

Question 5.
42

Explanation: The number which has more than two factors is called composite numbers.
Factors of 42 are: 1,2,3,6,7,21,42.

Tell whether the number is prime or composite.

Question 9.
64

Explanation: The number which has more than two factors is called a composite number.
Factors of 64 are 1,2,4,8,32,64.

Question 10.
33

Explanation: The number which has more than two factors is called a composite number.
Factors of 33 are: 1,3,11,33.

Question 11.
89

Explanation: A Prime number is a number that is divisible 1 and itself.

Question 12.
52

Explanation: The number which has more than two factors is called composite numbers.
Factors of 52 are: 1,2,4,13,26,52.

Question 13.
76

Explanation: The number which has more than two factors is called composite numbers.
Factors of 76 are: 1,2,4,19,38,76.

Write true or false for each statement. Explain or give an example to support your answer.

Question 14.
Only odd numbers are prime numbers.

Explanation: Not all odd numbers are prime numbers. For example. 39 is an odd number but not a prime number because it is divisible by 3 and 13.

Question 15.
A composite number cannot have three factors.

Explanation: A Composite number is a number that has more than two factors.
For example. 21 is a composite number and the factors of 21 are 1,3,7,21.

Question 16.
I am a number between 60 and 100. My ones digit is two less than my tens digit. I am a prime number. What number am I?

Explanation:
Prime numbers between 60 to 100 are 61,67,71,73,79,83,89,97. 97 is the number which ones digit is two less than tens digit.

Question 17.
Name a 2-digit odd number that is prime. Name a 2-digit odd number that is composite.

2 digit Prime odd numbers are 11,13,17 etc.
2 digit Composite odd numbers are 15,21,39

Explanation: A Prime number is a number that is divisible 1 and itself.
The number which has more than two factors is called composite numbers.

Question 18.
Choose the words that correctly complete the sentence.
The number 9 is img 18 because it has img 19 two factors.
Type below:
__________

### Page No. 308

The Sieve of Eratosthenes

Eratosthenes was a Greek mathematician who lived more than 2,200 years ago. He invented a method of finding prime numbers, which is now called the Sieve of Eratosthenes.

Question 19.
Follow the steps below to circle all prime numbers less than 100. Then list the prime numbers.
STEP 1
Cross out 1, since 1 is not prime.
STEP 2
Circle 2, since it is prime. Cross out all other multiples of 2.
STEP 3
Circle the next number that is not crossed out. This number is prime. Cross out all the multiples of this number.
STEP 4
Repeat Step 3 until every number is either circled or crossed out.

So, the prime numbers less than 100 are

Explanation: A Prime number is a number that is divisible 1 and itself.

Question 20.
Explain why the multiples of any number other than 1 are not prime numbers.

### Common Core – Prime and Composite Numbers – Page No. 309

Prime and Composite Numbers

Tell whether the number is prime or composite

Question 1.

Question 2.
68

Explanation: The number which has more than two factors is called composite numbers.
Factors of 68 are: 1,2,4,17,34,69.

Question 3.
52

Explanation: The number which has more than two factors is called composite numbers.
Factors of 52 are: 1,2,4,13,26,52.

Question 4.
63

Explanation: The number which has more than two factors is called composite numbers.
Factors of 63 are: 1,2,3,7,9,21,63.

Question 5.
75

Explanation: The number which has more than two factors is called composite numbers.
Factors of 75 are: 1,3,5,15,25,75

Question 6.
31

Explanation: 31 is a prime number that means it is divisible by 1 and itself.

Question 7.
77

Explanation: The number which has more than two factors is called composite numbers.
Factors of 77 are: 1,7,11,77.

Question 8.
59

Explanation: 59 is a prime number which means it is divisible by 1 and itself.

Question 11.
49

Explanation: The number which has more than two factors is called composite numbers.
Factors of 49 are 1,7,49.

Question 12.
73

Explanation: A Prime number is a number that is divisible 1 and itself.

Problem Solving

Question 13.
Kai wrote the number 85 on the board. Is 85 prime or composite?

Explanation: The number which has more than two factors is called composite numbers.
Factors of 85 are 1,5,17,85

Question 14.
Lisa says that 43 is a 2-digit odd number that is composite. Is she correct?

Explanation: 43 is a prime number. A Prime number is a number that is divisible 1 and itself.

### Common Core – Prime and Composite Numbers – Page No. 310

Lesson Check

Question 1.
The number 5 is:
Options:
a. prime
b. composite
c. both prime and composite
d. neither prime nor composite

Explanation: A Prime number is a number that is divisible 1 and itself.

Question 2.
The number 1 is:
Options:
a. prime
b. composite
c. both prime and composite
d. neither prime nor composite

Explanation: A Prime number is a number that is divisible 1 and itself. So prime number should have two divisors but 1 has only one divisor. The number which has more than two factors is called composite numbers. So 1 doesn’t have more than two factors. So 1 is neither Prime nor Composite.

Spiral Review

Question 3.
A recipe for a vegetable dish contains a total of 924 calories. The dish serves 6 people. How many calories are in each serving?
Options:
a. 134 calories
b. 150 calories
c. 154 calories
d. 231 calories

Explanation: Total no.of calories are 924, which serves 6 people. To find each serving we will perform division
924÷6= 154 calories.

Question 4.
A store clerk has 45 shirts to pack in  boxes. Each box holds 6 shirts. What is the fewest boxes the clerk will need to pack all the shirts?
Options:
a. 9
b. 8
c. 7
d. 6

Explanation: As the box holds only 6 shirts, 42 shirts are packed in 7 boxes, and the remaining 3 shirts will be packed in another box. So the total number of boxes is 8.

Question 5.
Which number rounds to 200,000?
Options:
a. 289,005
b. 251,659
c. 152,909
d. 149,889

Explanation: 152,909 is nearest to 200,000.

Question 6.
What is the word form of the number 602,107?
Options:
a. six hundred twenty thousand,seventeen
b. six hundred two thousand, one hundred seven
c. six hundred twenty-one thousand, seventeen
d. six hundred two thousand, one hundred seventy

### Page No. 313

Use the rule to write the numbers in the pattern.

Question 1.
Rule: Subtract 10. First term: 100

Explanation:
100
100-10= 90
90-10= 80
80-10= 70
70-10= 60

Use the rule to write the numbers in the pattern.
Describe another pattern in the numbers.

Question 2.
Rule: Multiply by 2. First term: 4
4 , _____ , _____ , _____ , _____ , …….

Explanation:
4
4×2= 8
8×2= 16
16×2= 32
32×2= 64

Question 3.
Rule: Skip-count by 6. First term: 12
12 , _____ , _____ , _____ , _____ , …….

Explanation:
12
12+6= 18
18+6= 24
24+6= 30
30+6= 36

Use the rule to write the first twelve numbers in the pattern. Describe another pattern in the numbers.

Question 4.
Rule: Add 7. First term: 3

3
3+7= 10
10+7= 17
17+7= 34
34+7= 41
41+7= 48
48+7= 55
55+7= 62
62+7= 69
69+7= 76
76+7= 83
83+7= 90.

Explanation: Added 7 to the given term.

Question 5.

Explanation:
12
12+2= 14
14+1= 15
15+2= 17
17+1= 19
19+2= 21
21+1= 22
22+2= 24
24+1= 25
25+2= 27
27+1= 28
28+2= 30
30+1= 31

Question 7.
John is saving for his trip to see the Alamo. He started with $24 in his savings account. Every week he earns$15 for babysitting. Out of that, he spends $8 and saves the rest. John uses the rule add 7 to find out how much money he has at the end of each week. What are the first 8 numbers in the pattern? Answer:$24, $31,$38, $45,$52, $59,$66, $73. Explanation: 24 24+7= 31 31+7= 38 38+7= 45 45+7= 52 52+7= 59 59+7= 66 66+7= 73. Question 8. Draw a check under the column that describes the number. Pose a Problem Question 9. Activity at the Math Fair shows two charts. Use at least two of the numbers and an operation from the charts to write a pattern problem. Include the first five terms of your pattern in the solution to your problem. Pose a problem. Solve your problem. Describe other patterns in the terms you wrote. Answer: 2+3= 5 Addition. 10-6= 4 Subtraction. 5×2= 10 Multiplication. ### Common Core – Number Patterns – Page No. 315 Number Patterns Use the rule to write the first twelve numbers in the pattern. Describe another pattern in the numbers. Question 1. Rule: Add 8. First term: 5 Question 2. Rule: Subtract 7. First term: 95 Answer: 95,88,81,74,67,60,53,46,39,32,25,118,11. Explanation: 95 95-7= 88 88-7= 81 81-7= 74 74-7= 67 67-7= 60 60-7= 53 53-7= 46 46-7= 39 39-7= 32 32-7= 25 25-7= 18 18-7= 11 Question 3. Rule: Add 15, subtract 10. First term: 4 Answer: 4,19,9,24,14,29,19,34,24,39,29,44,34. Explanation: 4 4+15= 19 19-10= 9 9+15= 24 24-10= 14 14+15= 29 29-10= 19 19+15= 34 34-10= 24 24+15= 39 39-10=29 29+15=44 44-10=34 Question 4. Rule: Add 1, multiply by 2. First term: 2 Answer: 2,4,5,10,11,22,23,46,47,94,95,190. Explanation: 2 2+1= 2 2×2= 4 4+1= 5 5×2= 10 10+1= 11 11×2= 22 22+1= 23 23×2= 46 46+1= 47 47×2= 94 94+1= 95 95×2= 190. Problem Solving ### Common Core – Number Patterns – Page No. 316 Lesson Check Question 1. The rule for a pattern is add 6. The first term is 5. Which of the following numbers is a term in the pattern? Options: a. 6 b. 12 c. 17 d. 22 Answer: c Explanation: 5 5+6= 11 11+6= 17 Question 2. What are the next two terms in the pattern 3, 6, 5, 10, 9, 18, 17, . . .? Options: a. 16, 15 b. 30, 31 c. 33, 34 d. 34, 33 Answer: d Explanation: 3 3×2= 6 6-1= 5 5×2= 10 10-1= 9 9×2= 18 18-1= 17 17×2= 34 34-1= 33 Spiral Review Question 3. To win a game, Roger needs to score 2,000 points. So far, he has scored 837 points. How many more points does Roger need to score? Options: a. 1,163 points b. 1,173 points c. 1,237 points d. 2,837 points Answer: a Explanation: Roger has scored 837 points, He needs to score 2000 points to win, So to know how much more points do Roger needs we need to subtract i.e 2,000-837= 1,163. Question 4. Sue wants to use mental math to find 7 × 53. Which expression could she use? Options: a. (7 × 5) + 3 b. (7 × 5) + (7 × 3) c. (7 × 50) + 3 d. (7 × 50) + (7 × 3) Answer: d Explanation: Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. Question 5. Pat listed numbers that all have 15 as a multiple. Which of the following could be Pat’s list? Options: a. 1, 3, 5, 15 b. 1, 5, 10, 15 c. 1, 15, 30, 45 d. 15, 115, 215 Answer: a Explanation: 1×15= 15 3×5= 15 5×3= 15 15×1= 15 Question 6. Which is a true statement about 7 and 14? Options: a. 7 is a multiple of 14. b. 14 is a factor of 7. c. 14 is a common multiple of 7 and 14. d. 21 is a common multiple of 7 and 14. Answer: c Explanation: 7×2=14 14×1=14 ### Review/Test – Page No. 317 Question 1. List all the factors of the number. 14: ______ , ______ , ______ , ______ Answer: 1,2,7,14 Explanation: Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 14 when multiplied together. So the factors of 14 are 1,2,7,14. Question 2. Select the numbers that have a factor of 5. Mark all that apply. Options: a. 15 b. 3 c. 45 d. 5 e. 50 f. 31 Answer: a,c,d,e. Explanation: Factors are the numbers that divide the original number completely. Question 3. Jackson was making a poster for his room. He arranged 50 trading cards in the shape of a rectangle on the poster. For 3a–3e, choose Yes or No to tell whether a possible arrangement of cards is shown. a. 5 rows of 10 cards i. yes ii. no Answer: Yes Explanation: 5 rows of 10 cards means 5×10= 50. So the answer is Yes. Question 3. b. 7 rows of 8 cards i. yes ii. no Answer: No Explanation: 7×8= 56, There will be extra cards. So the answer is No. Question 3. c. 25 rows of 2 cards i. yes ii. no Answer: Yes. Explanation: 25×2=50. So the answer is Yes Question 3. d. 50 rows of 1 card i. yes ii. no Answer: Yes Explanation: 50×1=50. So the answer is Yes. Question 3. e. 45 rows of 5 cards i. yes ii. no Answer: No Explanation: 45×5= 225. Which is not equal to 50. So the answer is No. Question 4. List all the factor pairs in the table. Answer: 1×48= 48 1,48 2×24= 48 2,24 3×16= 48 3,16 4×12= 48 4,12 6×8= 48 6,8 Explanation: Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 30 when multiplied together. ### Review/Test – Page No. 318 Question 5. Classify the numbers. Some numbers may belong in more than one box. Answer: Divisible by 5 and 9: 90 Divisible by 6 and 9: 54,72,90 Divisible by 2 and 6: 54,72,84,90,96 Question 6. James works in a flower shop. He will put 36 tulips in vases for a wedding. He must use the same number of tulips in each vase. The number of tulips in each vase must be greater than 1 and less than 10. How many tulips could be in each vase? Answer: 2, 3, 4, 6, 9. Explanation: Question 7. Brady has a card collection with 64 basketball cards, 32 football cards, and 24 baseball cards. He wants to arrange the cards in equal piles, with only one type of card in each pile. How many cards can he put in each pile? Mark all that apply. Options: a. 1 b. 2 c. 3 d. 4 e. 8 f. 32 Answer: a,b,d,e Explanation: Factors of 64 are 1,2,4,8,16,32,64. Factors of 32 are 1,2,4,8,16,32. Factors of 24 are 1,2,3,4,6,8,12,24. Common factors are 1,2,4,8. Question 8. The Garden Club is designing a garden with 24 cosmos, 32 pansies, and 36 marigolds. Each row will have only one type of plant in each row. Ben says he can put 6 plants in each row. He listed the common factors of 24, 32, and 36 below to support his reasoning. 24: 1, 2, 3, 4, 6, 8, 12, 24 32: 1, 2, 4, 6, 9, 16, 32 36: 1, 2, 3, 4, 6, 8, 12, 18, 36 Is he correct? Explain your answer. If his reasoning is incorrect, explain how he should have found the answer. Answer: No. He can put 1,2,4 plants in each row Explanation: The factors of 32 are incorrect. He listed as 6 and 9 are factors of 32 which is wrong and 8 is not a factor of 36. Factors of 32 are 1,2,4,8,16,32. Factors of 36 are 1,2,3,4,6,9,18,36. Common factors of 24,32 and 36 are 1,2,4. So he can put 1,2,4 plants in each row. ### Review/Test – Page No. 319 Question 9. Part A The museum is hosting a show for July that features the oil paintings by different artists. All artists show the same number of paintings and each will show more than 1 painting. How many artists could be featured in the show? Answer: 2,3,5,6,10,15 Explanation: Factors of 30 are 1,2,3,5,6,10,15,30. Question 9. Part B The museum wants to display all the art pieces in rows. Each row has the same number of pieces and the same type of pieces. How many pieces could be in each row? Explain how you found your answer. Answer: 1,3. Explanation: Factors of 30 are 1,2,3,5,6,10,15,30. Factors of 24 are 1,2,3,4,6,8,12,24 Factors of 21 are 1,3,7,21 Common Factors are 1,3 Question 10. Charles was skip counting at the Math Club meeting. He started to count by 8s. He said 8, 16, 24, 32, 40, and 48. What number will he say next? Answer: 56 Explanation: Multiples of 8 8×1= 8 8×2= 16 8×3= 24 8×4= 32 8×5= 40 8×6= 48 8×7= 56. ### Review/Test – Page No. 320 Question 12. For numbers, 12a–12e, select True or False for each statement. a. The number 36 is a multiple of 9. i. True ii. False Answer: True Explanation: 9×4= 36. Question 12. b. The number 3 is a multiple of 9. i. True ii. False Answer: False Explanation: Multiples of 9 are 9,18,27,36,45,54,63, etc. Question 12. c. The number 54 is a multiple of 9. i. True ii. False Answer: True Explanation: 9×6= 54 Question 12. d. The number 3 is a factor of 9. i. True ii. False Answer: True Explanation: Factors of 9 are 1,3,9. Question 12. e. The number 27 is a factor of 9. i. True ii. False Answer: True Explanation: Factors of 27 are 1,3,9,27 Question 14. Manny makes dinner using 1 box of pasta and 1 jar of sauce. If pasta is sold in packages of 6 boxes and sauce is sold in packages of 3 jars, what is the least number of dinners that Manny can make without any supplies leftover? Answer: 6 Manny has 1 box of pasta and 1 jar of sauce and he sold in a package of 6 boxes of pasta and 3 jars of sauce. Let the packages of pasta be 6P and jars of sauce be 3s. As Manny sold without any leftover 3S=6P, If we take 1 package of pasta then P=1, And 3S=6×1, where S= 6/3 which is equal to 2, So for every package of pasta, we need 2 packages of sauce, So the minimum purchase is 2 packages of sauce and 1 package of pasta. Since pasta packages are 6 boxes the minimum number of meals is 6. Question 15. Serena has several packages of raisins. Each package contains 3 boxes of raisins. Which could be the number of boxes of raisins Serena has? Mark all that apply. Options: a. 9 b. 18 c. 23 d. 27 e. 32 Answer: a,b,d Explanation: Factors of 3. Question 16. Choose the words that make the sentence true. The number 7 is because it has two factors. The number 7 is _________ because it has _________ two factors. Answer: The number 7 is a prime number because it has exactly two factors. Explanation: A Prime number is a number that is divisible 1 and itself. ### Review/Test – Page No. 321 Question 17. Winnie wrote the following riddle: I am a number between 60 and 100. My ones digit is two less than my tens digit. I am a prime number. Part A What number does Winnie’s riddle describe? Explain. Answer: 97 Explanation: 97 is the number which ones digit is two less than tens digit. Question 17. Part B Winnie’s friend Marco guessed that her riddle was about the number 79. Why can’t 79 be the answer to Winnie’s riddle? Explain. Answer: It’s wrong because in Winnie’s riddle ones digit is two less than tens digit. But in 79 ones digit is two greater than tens digit. Explanation: In 79 ones digit is two greater than tens digit. So Marco guess was incorrect. Question 18. Classify the numbers as prime or composite. Answer: Prime numbers are 37, 71 Composite numbers are 65, 82 Explanation: A Composite number is a number that has more than two factors. A Prime number is a number that is divisible 1 and itself. Question 19. Erica knits 18 squares on Monday. She knits 7 more squares each day from Tuesday through Thursday. How many squares does Erica knit on Friday? Answer: 46 squares. Explanation: 18 18+7= 25 25+7= 32 32+7= 39 39+7= 46. Question 20. Use the rule to write the first five terms of the pattern. Rule: Add 10, subtract 5 First term: 11 ______ ______ ______ ______ Answer: 11,21,16,26,21. Explanation: 11 11+10= 21 21-5= 16 16+10= 26 26-5= 21 ### Review/Test – Page No. 322 Question 21. Elina had 10 tiles to arrange in a rectangular design. She drew a model of the rectangles she could make with the ten tiles. Part A How does Elina’s drawing show that the number 10 is a composite number? Answer: 10 is a composite number because it has more than two factors. Explanation: The number which has more than two factors is called composite numbers. Question 21. Part B Suppose Elina used 15 tiles to make the rectangular design. How many different rectangles could she make with the 15 tiles? Write a list or draw a picture to show the number and dimensions of the rectangles she could make. Answer: 2 Explanation: one by 15 tiles and second by 3tiles in a row. Question 21. Part Cs Elina’s friend Luke said that he could make more rectangles with 24 tiles than with Elina’s 10 tiles. Do you agree with Luke? Explain. Answer: Yes Explanation: As 24 has more factors than 10. ### Page No. 329 Use the model to write an equivalent fraction. Question 1. $$\frac{1}{5}$$ = $$\frac{□}{□}$$ Answer: 1/5= 2/10 Explanation: From the above figure we can see that there are 5 equal parts and in that 1 part is shaded. So the fraction of the shaded part is 1/5. Question 2. $$\frac{2}{3}$$ = $$\frac{□}{□}$$ Answer: 2/3= 6/9 Explanation: From the above figure we can see that there are 3 equal parts and in that 2 part is shaded. So the fraction of the shaded part is 2/3. Tell whether the fractions are equivalent. Write = or ≠. Question 3. $$\frac{1}{6}$$ _____ $$\frac{2}{12}$$ Answer: 1/6=2/12 Explanation: The denominator and numerators are equal for both the fractions. So 1/6=2/12 are equal. Question 4. $$\frac{2}{5}$$ _____ $$\frac{6}{10}$$ Answer: 2/5≠ 6/10 Explanation: The denominator and numerators are not equal for both the fractions. Question 5. $$\frac{4}{12}$$ _____ $$\frac{1}{3}$$ Answer: 4/12=1/3 Explanation: The denominator and numerators are equal for both the fractions. Question 6. $$\frac{5}{8}$$ _____ $$\frac{2}{4}$$ Answer: 5/8≠2/4 Explanation: The denominator and numerators are not equal for both the fractions. Question 7. $$\frac{5}{6}$$ _____ $$\frac{10}{12}$$ Answer: 5/6=10/12 Explanation: The denominator and numerators are equal for both the fractions. Question 8. $$\frac{1}{2}$$ _____ $$\frac{5}{10}$$ Answer: 1/2=5/10 Explanation: The denominator and numerators are equal for both fractions. ### Page No. 330 Question 11. Ben brought two pizzas to a party. He says that since 14_ of each pizza is left, the same amount of each pizza is left. What is his error? Answer: As the size of pizzas is not the same, So 1/4 of leftover pizza is not equal to another. Question 12. For numbers, 12a–12d, tell whether the fractions are equivalent by selecting the correct symbol. a. $$\frac{3}{15}$$ _____ $$\frac{1}{6}$$ Answer: 3/5≠1/6 Question 12. b. $$\frac{3}{4}$$ _____ $$\frac{16}{20}$$ Answer: 3/4≠16/20 Question 12. c. $$\frac{2}{3}$$ _____ $$\frac{8}{12}$$ Answer: 2/3=8/12 Question 12. d. $$\frac{4}{5}$$ _____ $$\frac{8}{10}$$ Answer: 4/5=8/10. ## Go Math Grade 4 Answer Key Chapter 4 Divide by 1-Digit Numbers Go Math Grade 4 Answer Key Chapter 4 Divide by 1-Digit Numbers is the most important learning guide to learn the subject properly. It is a quick preparation & practice purpose material for students and educators. So, We have provided the solutions for all the questions with a brief explanation in this Go Math HMH Grade 4 Chapter 4 Answer Key. All these solutions are prepared by the Math Experts. Students and parents are suggested to Download Go Math Grade 4 Answer Key Chapter 4 Divide by 1-Digit Numbers pdf from here for free. ## Go Math Grade 4 Answer Key Chapter 4 Divide by 1-Digit Numbers Avail all detailed solutions to the questions via Go Math Answer Key of grade 4 chapter 4 and aid while doing homework and also while preparing for the exams. Just tap on the respective lesson link from chapter 4 Divide by 1-Digit Numbers and solve the questions. Along with the exercise and homework problems, we have also listed the answers for the mid-chapter checkpoint and review test in the Go Math Grade 4 Solution Key Chapter 4 Divide by 1-Digit Numbers. Chapter 4 Divide by 1-Digit Numbers – Lesson: 1 Chapter 4 Divide by 1-Digit Numbers – Lesson: 2 Chapter 4 Divide by 1-Digit Numbers – Lesson: 3 Chapter 4 Divide by 1-Digit Numbers – Lesson: 4 Chapter 4 Divide by 1-Digit Numbers – Lesson: 5 Chapter 4 Divide by 1-Digit Numbers – Lesson: 6 Chapter 4 Divide by 1-Digit Numbers – Lesson: 7 Chapter 4 Divide by 1-Digit Numbers – Lesson: 8 Chapter 4 Divide by 1-Digit Numbers – Lesson: 9 Chapter 4 Divide by 1-Digit Numbers – Lesson: 10 Chapter 4 Divide by 1-Digit Numbers – Lesson: 11 Mid Chapter Checkpoint Chapter 4 Divide by 1-Digit Numbers – Lesson: 12 Chapter 4 Divide by 1-Digit Numbers – Lesson: 13 Chapter 4 Divide by 1-Digit Numbers – Lesson: 14 Chapter 4 Divide by 1-Digit Numbers – Lesson: 15 Chapter 4 Divide by 1-Digit Numbers – Lesson: 16 Chapter 4 Divide by 1-Digit Numbers – Lesson: 17 Chapter 4 Divide by 1-Digit Numbers – Lesson: 18 Chapter 4 Divide by 1-Digit Numbers – Lesson: 19 Chapter 4 Divide by 1-Digit Numbers – Lesson: 20 Chapter 4 Divide by 1-Digit Numbers – Lesson: 21 Chapter 4 Divide by 1-Digit Numbers – Lesson: 22 Chapter 4 Divide by 1-Digit Numbers – Lesson: 23 Chapter 4 – Review/Test ### Common Core – Page No. 201 Estimate Quotients Using Multiples Find two numbers the quotient is between. Then estimate the quotient. Question 1. 175 ÷ 6 Think: 6 × 20 = 120 and 6 × 30 = 180. So, 175 ÷ 6 is between 20 and 30. Since 175 is closer to 180 than to 120, the quotient is about 30. between 20 and 30 about 30 Answer: About 30 Explanation: 6 × 20 = 120 and 6 × 30 = 180. 175 is between 120 and 180. 175 ÷ 6 is closest to 20 and 30. So, 175 ÷ 6 is between 20 and 30. So, 175 ÷ 6 will be about 30. Question 2. 53 ÷ 3 between ______ and about ______ Answer: About 18 Explanation: 17 × 3= 51 and 18 × 3 = 54. 53 is between 51 and 54. 53 ÷ 3 is closest to 17 and 18. So, 53 ÷ 3 is between 17 and 18. So, 53 ÷ 3 will be about 18. Question 3. 75 ÷ 4 between ______ and about ______ Answer: About 19 Explanation: 18 × 4= 72 and 19 × 4= 76. 75 is between 72 and 76. 75 ÷ 4 is closest to 18 and 19. So, 75÷ 4 is between 18 and 19. So, 75 ÷ 4 will be about 19. Question 6. 191 ÷ 3 between ______ and about ______ Answer: About 64 Explanation: 63 × 3 = 189 and 64 × 3 = 192. 191 is between 189 and 192. 191 ÷ 3 is closest to 63 and 64. So, 191 ÷ 3 is between 63 and 64. So, 175 ÷ 6 will be about 64. Question 7. 100 ÷ 7 between ______ and about ______ Answer: About 14 Explanation: 14 × 7 = 98 and 15 × 7 = 105. 100 is between 98 and 105. 100 ÷ 7 is closest to 14 and 15. So, 100 ÷ 7 is between 14 and 15. So, 100 ÷ 7 will be about 14. Question 8. 438 ÷ 7 between ______ and about ______ Answer: About 63 Explanation: 63 × 7 = 441 and 62 × 7 = 434. 438 is between 434 and 441. 438 ÷ 7 is closest to 62 and 63. So, 438 ÷ 7 is between 62 and 63. So, 438 ÷ 7 will be about 63. Question 9. 103 ÷ 8 between ______ and about ______ Answer: About 13 Explanation: 13 × 8 = 104 and 12 ×8 = 96. 103 is between 96 and 104. 103 ÷ 8 is closest to 12 and 13. So, 103 ÷ 8 is between 12 and 13. So, 103 ÷ 8 will be about 13. Question 10. 255 ÷ 9 between ______ and about ______ Answer: About 28 Explanation: 28 × 9 = 252 and 29 × 9 = 261. 255 is between 252 and 261. 255 ÷ 9 is closest to 28 and 29. So, 255 ÷ 9 is between 28 and 29. So, 255 ÷ 9 will be about 28. Problem Solving ### Common Core – Page No. 202 Lesson Check Question 1. Abby did 121 sit-ups in 8 minutes. Which is the best estimate of the number of sit-ups she did in 1 minute? Options: a. about 12 b. about 15 c. about 16 d. about 20 Answer: b. About 15 Explanation: 15 × 8 = 120 and 16 × 8 = 128. 121 is between 120 and 128. 121 ÷ 8 is closest to 120 and 128. So, 121 ÷ 8 is between 15 and 16. So, 121 ÷ 8 will be about 15. Question 2. The Garibaldi family drove 400 miles in 7 hours. Which is the best estimate of the number of miles they drove in 1 hour? Options: a. about 40 miles b. about 57 miles c. about 60 miles d. about 70 miles Answer: b. About 57 miles Explanation: 57 × 7 = 399 and 58 × 7 = 406. 400 is between 399 and 406. 400 ÷ 7 is closest to 57 and 58. So, 400 ÷ 7 is between 57 and 58. So, 400 ÷ 7 will be about 57. Spiral Review Question 3. Twelve boys collected 16 aluminium cans each. Fifteen girls collected 14 aluminium cans each. How many more cans did the girls collect than the boys? Options: a. 8 b. 12 c. 14 d. 18 Answer: 18 Explanation: Number of aluminium cans boys had= 12× 16=192 Number of aluminium cans girls had = 15× 14=210 Girls collected more cans compared to boys, Number of more cans collected by girls= 210-192=18 Question 4. George bought 30 packs of football cards. There were 14 cards in each pack. How many cards did George buy? Options: a. 170 b. 320 c. 420 d. 520 Answer: c. 420 Explanation: Number of packs of football cards= 30 Number of cards in each pack= 14 Total number of cards George bought=30×14=420 Question 5. Sarah made a necklace using 5 times as many blue beads as white beads. She used a total of 30 beads. How many blue beads did Sarah use? Options: a. 5 b. 6 c. 24 d. 25 Answer: d. 25 Explanation: Let the number of white beads be x while the number of blue beads are 5x. Total number of beads in the necklace=30 beads According to the problem, 5x+x=30 6x=30 x=30/6=5 Therefore the number of blue beads in the necklace are 5x= 5×5=25 Question 6. This year, Ms. Webster flew 145,000 miles on business. Last year, she flew 83,125 miles on business. How many more miles did Ms. Webster fly on business this year? Options: a. 61,125 miles b. 61,875 miles c. 61,985 miles d. 62,125 miles Answer: b. 61,875 miles Explanation: Number of miles Ms Webster flew in this year= 145,000 miles Number of miles Ms Webster flew in the last year=83,125 miles Number of more miles travelled by Ms Webster =145,000-83,125=61,875 ### Page No. 205 Use counters to find the quotient and remainder. Question 1. 10 ÷ 3 _____ R ______ Answer: Quotient: 3 Remainder: 1 Explanation: Quotient: A. Use 10 counters to represent the 10 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of groups of counters formed = quotient of 10 ÷ 3 D. Number of circles equally filled are 3, therefore, the quotient is 3 Remainder: The number of counters left over is the remainder. The number of counters leftover= 1 For 10 ÷ 3, the quotient is 3 and the remainder is 1, or 3 r1. Question 2. 28 ÷ 5 _____ R ______ Answer: Quotient: 5 Remainder: 3 Explanation: Quotient: A. Use 28 counters to represent the 28 dominoes. Then draw 5 circles to represent the divisor. B. Share the counters equally among the 5 groups by placing them in the circles. C. Number of groups of counters formed = quotient of 28÷ 5 Remainder: The number of counters left over is the remainder. The number of counters leftover= 3 For 28 ÷ 5, the quotient is 5 and the remainder is 3, or 5 r3. Question 3. 15 ÷ 6 _____ R ______ Answer: Quotient:2 Remainder:3 Explanation: Quotient: A. Use 15 counters to represent the 15 dominoes. Then draw 6 circles to represent the divisor. B. Share the counters equally among the 6 groups by placing them in the circles. C. Number of circles filled= quotient of 28 ÷ 6 Remainder: The number of counters left over is the remainder. The number of counters leftover= 3 For 28 ÷ 6, the quotient is 2 and the remainder is 3, or 2 r3. Question 4. 11 ÷ 3 _____ R ______ Answer:Quotient:3 Remainder:2 Explanation: Quotient: A. Use 11 counters to represent the 3 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of circles filled = quotient of 11 ÷ 3 Remainder: The number of counters left over is the remainder. The number of counters leftover= 2 For 11 ÷ 3, the quotient is 3 and the remainder is 2, or 3 r2. Question 7. 25 ÷ 3 _____ R ______ Answer:Quotient: 8 Remainder: 1 Explanation: Quotient: A. Use 25 counters to represent the 25 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of circles filled= quotient of 25 ÷ 3 Remainder: The number of counters left over is the remainder. The number of counters leftover= 1 For 25 ÷ 3, the quotient is 8 and the remainder is 1, or 8 r1. Question 8. 7)$$\overline { 20 }$$ _____ R ______ Answer: Quotient:2 Remainder:6 Explanation: Quotient: A. Use 20 counters to represent the 20 dominoes. Then draw 7 circles to represent the divisor. B. Share the counters equally among the 7 groups by placing them in the circles. C. Number of circles filled= quotient of 7 qw20 Remainder: The number of counters left over is the remainder. The number of counters leftover= 1 Divide. Draw a quick picture to help. Question 9. 4)$$\overline { 35 }$$ _____ R ______ Answer: Quotient: 8 Remainder:3 Explanation: Quotient: A. Use 35 counters to represent the 35 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of circles filled= quotient of $$\overline { 35 }$$=8 Remainder: The number of counters left over is the remainder. The number of counters leftover= 3 Question 10. 23 ÷ 8 _____ R ______ Answer: Quotient: 2 Remainder: 7 Explanation: Quotient: A. Use 23 counters to represent the 23 dominoes. Then draw 8 circles to represent the divisor. B. Share the counters equally among the 8 groups by placing them in the circles. C. Number of circles filled= quotient of 23 ÷ 8 = 2 Remainder: The number of counters left over is the remainder. The number of counters leftover= 7 Question 11. Explain how you use a quick picture to find the quotient and remainder. Type below: _________ Answer: Quick pictures can be used to find the quotient and the remainder visually and accurately. Explanation: Example: 39÷ 5. Use 39 counters. Share the counters equally among 5 groups. The number of counters left over is the remainder. For 39 ÷ 5, the quotient is 7 and the remainder is 2, or 7 r2. When a number cannot be divided evenly, the amount left over is called the remainder. Question 12. Alyson has 46 beads to make bracelets. Each bracelet has 5 beads. How many more beads does Alyson need so that all the beads she has are used? Explain. _____ more beads Answer: 4 beads Explanation: Number of beads Alyson has= 46 Number of beads each bracelet needs=5 The number of bracelets which can be made = 46÷5 Since the remainder is one we can say that one bead is leftover after making 9 bracelets. Therefore, 4 beads should be added to 1 so that all the beads are used up. Question 13. For 13a–13d, choose Yes or No to tell whether the division expression has a remainder. a. 36 ÷ 9 i. yes ii. no Answer: ii. no Explanation: Question 13. b. 23 ÷ 3 i. yes ii. no Answer: i. yes Explanation: Question 13. c. 82 ÷ 9 i. yes ii. no Answer: i. yes Explanation: Question 13. d. 28 ÷ 7 i. yes ii. no Answer: ii. no Explanation: ### Page No. 206 Question 14. Macy, Kayley, Maddie, and Rachel collected 13 marbles. They want to share the marbles equally. How many marbles will each of the 4 girls get? How many marbles will be left over? Oscar used a model to solve this problem. He says his model represents 4)$$\overline { 13 }$$. What is his error? Look at the way Oscar solved this problem. Find and describe his error. _________________________________________________________ Draw a correct model and solve the problem. So, each of the 4 girls will get _______ marbles and _______ marble will be left over. Type below: _________ Answer: Quotient: 3 Remainder: 1 Explanation: Quotient: A. Use 13 counters to represent the 13 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of circles filled= quotient of 13 ÷ 4 = 3 Remainder: The number of counters left over is the remainder. The number of counters leftover= 1 Therefore each girl will get 3 marbles. ### Common Core – Page No. 207 Remainders Use counters to find the quotient and remainder. Question 1. 13 ÷ 4 3 r1 Answer: 3 r1 Explanation: Quotient: A. Use 13 counters to represent the 13 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 13 ÷ 4 D. Number of circles are equally filled with 4 counters, therefore, the quotient is 3 Remainder: The number of counters left over is the remainder. The number of counters leftover= 1 For 13 ÷ 4, the quotient is 3 and the remainder is 1, or 3 r1. Question 2. 24 ÷ 7 _____ R ______ Answer: 3 r3 Explanation: Quotient: A. Use 24 counters to represent the 24 dominoes. Then draw 7 circles to represent the divisor. B. Share the counters equally among the 7 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 24 ÷ 7 D. Number of circles are equally filled with 3 counters, therefore, the quotient is 3 Remainder: The number of counters left over is the remainder. The number of counters leftover= 3 For 24 ÷ 7, the quotient is 3 and the remainder is 3, or 3 r3. Question 5. 6)$$\overline { 27 }$$ _____ R ______ Answer: 4 r3 Explanation: Quotient: A. Use 27 counters to represent the 27 dominoes. Then draw 6 circles to represent the divisor. B. Share the counters equally among the 6 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 27 ÷6 D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4 Remainder: The number of counters left over is the remainder. The number of counters leftover= 3 For 27 ÷ 6, the quotient is 4 and the remainder is 3, or 4 r3. Question 6. 25 ÷ 9 _____ R ______ Answer: 2 r7 Explanation: Quotient: A. Use 25 counters to represent the 25 dominoes. Then draw 9 circles to represent the divisor. B. Share the counters equally among the 9 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 25 ÷ 9 D. Number of circles are equally filled with 2 counters, therefore, the quotient is 2 Remainder: The number of counters left over is the remainder. The number of counters leftover= 7 For 25 ÷ 7, the quotient is 2 and the remainder is 7, or 2 r7. Question 7. 3)$$\overline { 17 }$$ _____ R ______ Answer: 5 r2 Explanation: Quotient: A. Use 17 counters to represent the 17 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 17 ÷ 3 D. Number of circles are equally filled with 5 counters, therefore, the quotient is 5 Remainder: The number of counters left over is the remainder. The number of counters leftover= 2 For 17 ÷ 3, the quotient is 5 and the remainder is 2, or 5 r2. Question 8. 26 ÷ 4 _____ R ______ Answer: 6 r2 Explanation: Quotient: A. Use 26 counters to represent the 26 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 26 ÷ 4 D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6 Remainder: The number of counters left over is the remainder. The number of counters leftover= 2 For 26 ÷ 4, the quotient is 6 and the remainder is 2, or 6 r2. Divide. Draw a quick picture to help. Question 9. 14 ÷ 3 _____ R ______ Answer: Quotient: 4 Remainder: 2 Explanation: Quotient: A. Use 14 counters to represent the 14 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of circles filled= quotient of 14 ÷ 3 = 4 Remainder: The number of counters left over is the remainder. The number of counters leftover= 2 Question 10. 5)$$\overline { 29 }$$ _____ R ______ Answer: Quotient: 5 Remainder: 4 Explanation: Quotient: A. Use 29 counters to represent the 29 dominoes. Then draw 5 circles to represent the divisor. B. Share the counters equally among the 5 groups by placing them in the circles. C. Number of circles filled= quotient of 29 ÷ 5 = 5 Remainder: The number of counters left over is the remainder. The number of counters leftover= 4 Problem Solving Question 11. What is the quotient and remainder in the division problem modeled below? _____ R ______ Answer: quotient:6 remainder2 Explanation: Quotient: A. Use 20 counters to represent the 20 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 20 ÷ 3 D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6 Remainder: The number of counters left over is the remainder. The number of counters leftover= 2 For 20 ÷ 3, the quotient is 6 and the remainder is 2, or 6 r2. Question 12. Mark drew the following model and said it represented the problem 21 ÷ 4. Is Mark’s model correct? If so, what is the quotient and remainder? If not, what is the correct quotient and remainder? _____ ; _____ r Answer: 4 r5 Explanation: Quotient: A. Use 21 counters to represent the 21 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 21 ÷ 4 D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4 Remainder: The number of counters left over is the remainder. The number of counters leftover= 5 For 21 ÷ 4, the quotient is 4 and the remainder is 5, or 4 r5. ### Common Core – Page No. 208 Lesson Check Question 1. What is the quotient and remainder for 32 ÷ 6? Options: a. 4 r3 b. 5 r1 c. 5 r2 d. 6 r1 Answer: c. 5 r2 Explanation: Quotient: A. Use 32 counters to represent the 32 dominoes. Then draw 6 circles to represent the divisor. B. Share the counters equally among the 5 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 32 ÷ 6 D. Number of circles are equally filled with 5 counters, therefore, the quotient is 5 Remainder: The number of counters left over is the remainder. The number of counters leftover= 2 For 32 ÷ 6, the quotient is 5 and the remainder is 2, or 5 r2. Question 2. What is the remainder in the division problem modeled below? Options: a. 8 b. 4 c. 3 d. 1 Answer: c. 3 Explanation: When a number cannot be divided evenly, the amount left over is called the remainder. The number of counters that are left = remainder = 3 Spiral Review Question 3. Each kit to build a castle contains 235 parts. How many parts are in 4 of the kits? Options: a. 1,020 b. 940 c. 920 d. 840 Answer: b. 940 Explanation: Number of parts used to build a castle in each kit=235 parts Number of kits= 4 Total number of parts in 4 of the kits= 235 x 4=940 parts Question 4. In 2010, the population of Alaska was about 710,200. What is this number written in word form? Options: a. seven hundred ten thousand, two b. seven hundred twelve thousand c. seventy-one thousand, two d. seven hundred ten thousand, two hundred Answer: d. seven hundred ten thousand, two hundred Explanation: The ones and tens place of the number are zeroes, so the next place which is hundreds is considered and the value is 7 so, it can be written as seven hundred and in the thousands period it can be written as seven hundred ten thousand. Question 5. At the theater, one section of seats has 8 rows with 12 seats in each row. In the center of the first 3 rows are 4 broken seats that cannot be used. How many seats can be used in the section? Options: a. 84 b. 88 c. 92 d. 96 Answer: c. 92 Explanation: Number of rows at the theatre = 8 Number of seats each row= 12 Number of seats broken and that cannot be used to sit= 4 Total number of seats that can be used= 12 x 8-4=96-4=92 Question 6. What partial products are shown by the model below? Options: a. 300, 24 b. 300, 600, 40, 60 c. 300, 60, 40, 24 d. 300, 180, 40, 24 Answer: d. 300, 180, 40, 24 Explanation: The whole rectangle is divided into four small rectangles the areas of these rectangles are: Area of yellow rectangle= 30 x 10=300 Area of green rectangle= 4 x 10 = 40 Area of pink rectangle= 6 x 30= 180 Area of blue rectangle= 4 x 6= 24 ### Common Core – Page No. 211 Question 1. Olivia baked 53 mini-loaves of banana bread to be sliced for snacks at a craft fair. She will place an equal number of loaves in 6 different locations. How many loaves will be at each location? a. Divide to find the quotient and remainder. □ r □ 6)$$\overline { 53 }$$ _____ R ______ Answer: Quotient: 8 Remainder: 5 Explanation: Quotient: A. Use 53 counters to represent the 53 dominoes. Then draw 6 circles to represent the divisor. B. Share the counters equally among the 6 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 53 ÷ 6 D. Number of circles are equally filled with 8 counters, therefore, the quotient is 8 Remainder: The number of counters left over is the remainder. The number of counters leftover= 5 Therefore, there will be 8 loaves at each location. Question 1. b. Decide how to use the quotient and remainder to answer the question. Type below: ____________ Answer: The quotient is used to determine the number of loaves at each location, while the remainder gives us the information about the number of loaves left after placing in different locations. Explanation: Quotient: A. Use 53 counters to represent the 53 dominoes. Then draw 6 circles to represent the divisor. B. Share the counters equally among the 6 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 53 ÷ 6 D. Number of circles are equally filled with 8 counters, therefore, the quotient is 8 Remainder: The number of counters left over is the remainder. The number of counters leftover= 5 Therefore, there will be 8 mini loaves at each location. Interpret the remainder to solve. Question 2. What if Olivia wants to put only whole loaves at each location? How many loaves will be at each location? _______ whole loaves Answer: Since there are 8 mini loaves at each location. Then there will be 4 whole loaves. Explanation: Olivia baked 53 mini-loaves of banana bread Interpret the remainder to solve. Question 4. Myra has a 17-foot roll of crepe paper to make 8 streamers to decorate for a party. How long will each streamer be if she cuts the roll into equal pieces? Type below: ____________ Answer: 2 foot Explanation: Length of the crepe paper = 17 foot Number of streamers in the party=8 Length of each part if they are cut into equal pieces = 17 ÷ 8 Question 5. Juan has a piano recital next month. Last week he practiced for 8 hours in the morning and 7 hours in the afternoon. Each practice session is 2 hours long. How many full practice sessions did Juan complete? _______ full practice sessions Answer: 7 full practice sessions Explanation: Number of hours he practiced in the morning= 8 hours Each practice session is 2 hours long Number of full practice sessions attended by Juan in the morning= 8÷2=4 Number of hours he practiced in the afternoon= 7 hours Number of full practice sessions attended by Juan in the evening= 7÷2=3 ### Page No. 212 Use the picture for 7–9. Question 7. Teresa is making sock puppets just like the one in the picture. If she has 53 buttons, how many puppets can she make? _______ sock puppets Answer: 17 sock puppets Explanation: Total number of buttons Teresa has=53 Number of buttons each puppet needs= 3 Number of sock puppets made= Quotient of 53÷3=17 sock puppets Question 8. Write a question about Teresa and the sock puppets for which the answer is 3. Explain the answer. Type below: ____________ Answer: How many buttons did Teresa use for one sock puppet? Explanation: Total number of sock puppets made= 17 Number of buttons used for making 17 sock puppets = 52 then, Number of buttons used for one sock puppet= Quotient of 52÷17= 3 buttons Question 9. Interpret a Result How many more buttons will Teresa need if she wants to make 18 puppets? Explain. _______ buttons Answer: 1 button Explanation: After preparing 17 puppets there were 2 buttons leftover then on the addition of 1 button gives 3 buttons which can be used to prepare another puppet. Question 10. A total of 56 students signed up to play in a flag football league. If each team has 10 students, how many more students will need to sign up so all of the students can be on a team? _______ students Answer: 4 students Explanation: Total number of students in the football league= 56 Number of students in each group= 10 then, Number of groups= Quotient of 56÷10=5 groups Remainder= 6 By the addition of 4 students, the group of 6 gets completed by 10 Therefore, 4 students should be added so that all students can be on a team. Question 11. A teacher plans for groups of her students to eat lunch at tables. She has 34 students in her class. Each group will have 7 students. How many tables will she need? Explain how to use the quotient and remainder to answer the question. _______ tables Answer: She needs 3 tables Explanation: Quotient: A. Use 34 counters to represent the 34 dominoes. Then draw 7 circles to represent the divisor. B. Share the counters equally among the 7 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 34 ÷ 7 D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4 Remainder: The number of counters left over is the remainder. The number of counters leftover= 6 The quotient is used to indicate the number of groups Therefore, there will be 4 tables. While the remainder is used to determine the number of students in the incomplete group. ### Common Core – Page No. 213 Interpret the Remainder Interpret the remainder to solve. Question 1. Hakeem has 100 tomato plants. He wants to plant them in rows of 8. How many full rows will he have? Think: 100 ÷ 8 is 12 with a remainder of 4. The question asks “how many full rows,” so use only the quotient. 12 full rows Answer: 12 full rows Explanation: Quotient: A. Use 100 counters to represent the 100 dominoes. Then draw 8 circles to represent the divisor. B. Share the counters equally among the 8 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 100 ÷ 8 D. Number of circles are equally filled with 12 counters, therefore, the quotient is 12 Therefore, the tomatoes placed in full rows are 12 Question 2. A teacher has 27 students in her class. She asks the students to form as many groups of 4 as possible. How many students will not be in a group? _______ students Answer: 3 students will not be the group Explanation: Total number of students in the class= 27 Number of students who make a group=4 Number of groups that can be made =Quotient of 27÷ 4=6 Number of students who do not come under a group= Remainder of 27÷ 4=3 Question 3. A sporting goods company can ship 6 footballs in each carton. How many cartons are needed to ship 75 footballs? _______ cartons Answer: 12 full cartons and 0.5 or 1/2 carton to ship all the 75 footballs Explanation: Total number of footballs that should be shipped= 75 Number of footballs placed in each carton = 6 Number of cartons required=Quotient of 75÷ 6=12 Since each carton carries 6 balls, half carton contains 3 balls because 6÷3=2, therefore, each half of the carton contains 3 balls. Problem Solving Question 6. Joanna has 70 beads. She uses 8 beads for each bracelet. She makes as many bracelets as possible. How many beads will Joanna have left over? _______ beads Answer: 6 beads Explanation: Total number of beads Joanna has= 70 beads Number beads used for each bracelet= 8 beads Number of bracelets made with these beads= Quotient of 70÷8= 7 bracelets then, The number of beads leftover= Remainder of 70÷8= 6 beads Question 7. A teacher wants to give 3 markers to each of her 25 students. Markers come in packages of 8. How many packages of markers will the teacher need? _______ packages Answer: 10 packages Explanation: Total number of students= 25 Number of markers each student got= 3 Total number of markers the teacher needs to distribute= 25 x 3= 75 Number of markers in each package= 8 Number of packages the teacher required= Quotient of 75÷8=9 While the remainder= 3 Therefore the total number packages=10 ### Common Core – Page No. 214 Lesson Check Question 1. Marcus sorts his 85 baseball cards into stacks of 9 cards each. How many stacks of 9 cards can Marcus make? Options: a. 4 b. 8 c. 9 d. 10 Answer: d. 10 Explanation: Total number of baseball cards=85 Number of cards in each stack=9 Number of stacks sorted= Quotient of 85÷9=9 While the remainder=4 So the total number of stacks required= 10 Question 2. A minivan can hold up to 7 people. How many minivans are needed to take 45 people to a basketball game? Options: a. 3 b. 5 c. 6 d. 7 Answer: d. 7 Explanation: A minivan can hold up to 7 people. Total number of people who want to hire the minivan= 45 people Number of minivans required= Quotient of 45÷7= 6 vans While the remainder is 3. Total number of minivans required to take the people to the baseball game= 7 minivans Spiral Review Question 3. Mrs. Wilkerson cut some oranges into 20 equal pieces to be shared by 6 friends. How many pieces did each person get and how many pieces were left over? Options: a. 2 pieces with 4 pieces leftover b. 3 pieces with 2 pieces leftover c. 3 pieces with 4 pieces leftover d. 4 pieces with 2 pieces leftover Answer: b. 3 pieces with 2 pieces leftover Explanation: Total number of orange pieces= 20 Number of friends= 6 Number of pieces each friend got= Quotient of 20÷6= 3 pieces Number of pieces leftover= Remainder of 20÷6= 2 pieces Question 4. A school bought 32 new desks. Each desk cost$24. Which is the best estimate of how much the school spent on the new desks?
Options:
a. $500 b.$750
c. $1,000 d.$1,200

Answer: b. $750 Explanation: Total number of desks= 32 Cost of each desk=$24
Total cost spent on the desks= 32 x 24=$768 So the estimated value can be$768

Question 5.
Kris has a box of 8 crayons. Sylvia’s box has 6 times as many crayons as Kris’s box. How many crayons are in Sylvia’s box?
Options:
a. 48
b. 42
c. 36
d. 4

Explanation:
Number of crayons in Kris box=8
Number of crayons in Sylvia’s box= 6 times as many crayons as Kris’s box= 6 x 8=48

Question 6.
Yesterday, 1,743 people visited the fair. Today, there are 576 more people at the fair than yesterday. How many people are at the fair today?
Options:
a. 1,167
b. 2,219
c. 2,319
d. 2,367

Explanation:
Number of people in the fair yesterday= 1,743
Number of more people at the fair than yesterday= 576
Total number of people in the fair today=2,319

### Page No. 216

Question 1.
Divide. 2,800 ÷ 7
What basic fact can you use? ___________
2,800 = 28 ___________
28 hundreds ÷ 7 = ___________
2,800 ÷ 7 = ___________
Type below:
___________

Explanation:
STEP 1 Identify the basic fact. 28 ÷ 7
STEP 2 Use place value. 2,800 = 28 hundreds
STEP 3 Divide. 28 hundreds ÷ 4 = 4 hundreds
2,800 ÷ 7 = 400

Question 2.
Divide. 280 ÷ 7
What basic fact can you use? ___________
280 = 28 ___________
28 tens ÷ _____ = 4 ___________
280 ÷ 7 = _____
Type below:
___________

Explanation:
STEP 1 Identify the basic fact. 28 ÷ 7
STEP 2 Use place value. 280 = 28 tens
STEP 3 Divide. 28 tens ÷ 4 = 4 tens
280 ÷ 7 = 40

Use basic facts and place value to find the quotient.

Question 5.
4,500 ÷ 9 = ______

Explanation:
STEP 1 Identify the basic fact. 45 ÷ 9
STEP 2 Use place value. 4,500 = 45 hundreds
STEP 3 Divide. 45 hundreds ÷ 9 = 5 hundreds
4,500 ÷ 9 = 500

Question 6.
560 ÷ 8 = ______

Explanation:
STEP 1 Identify the basic fact. 56 ÷ 8
STEP 2 Use place value. 560 = 56 tens
STEP 3 Divide. 56 tens ÷ 8 = 7 tens
560 ÷ 8 = 70

Question 7.
6,400 ÷ 8 = ______

Explanation:
STEP 1 Identify the basic fact. 64 ÷ 8
STEP 2 Use place value. 6,400 =64 hundreds
STEP 3 Divide. 64 hundreds ÷ 8 = 8 hundreds
6,400 ÷ 8 = 800

Question 8.
3,500 ÷ 7 = ______

Explanation:
STEP 1 Identify the basic fact. 35 ÷ 7
STEP 2 Use place value. 3,500 = 35 hundreds
STEP 3 Divide. 35 hundreds ÷ 7 = 5 hundreds
3,500 ÷ 7 = 500

Use Patterns Algebra Find the unknown number.

Question 9.
420 ÷ ______ = 60

Explanation:
To find the divisor (the missing number) divide 420 with 60

Therefore the quotient of 420 ÷ 60= The missing number=7

Question 10.
______ ÷ 4 = 30

Explanation:
To find the dividend (the missing number) we must multiply the divisor and the quotient.
Therefore the dividend is 30 x 4=120.

Question 11.
810 ÷ ______ = 90

Explanation:
To find the divisor (the missing number) divide 810 with 90

Therefore the quotient of 810 ÷ 90= The missing number=9

Question 12.
Divide 400 ÷ 40. Explain how patterns and place value can help.
______

Explanation:
STEP 1 Identify the basic fact. 40 ÷ 4
STEP 2 Use place value. 400 = 40 tens
STEP 3 Divide. 40 tens ÷ 4 = 1 tens
400 ÷ 40 = 10

### Page No. 217

Question 15.
Jamal put 600 pennies into 6 equal rolls. How many pennies were in each roll?

______ pennies

Explanation:
Total number of pennies= 600
Number of rolls= 6
The number of pennies= Quotient of 600 ÷ 6=100

Question 16.
Sela has 6 times as many coins now as she had 4 months ago. If Sela has 240 coins now, how many coins did she have 4 months ago?
______ coins

Explanation:
Let the number of coins four months ago be x coins.
According to the question,
Number of coins Sela has at present = 4x
4x=240
x= 240 ÷ 4=60
Therefore the number of coins Sela has=60

Question 17.
Chip collected 2,090 dimes. Sue collected 1,910 dimes. They divided all their dimes into 8 equal stacks. How many dimes are in each stack?
______ dimes

Explanation:
Number of dimes Chip collected= 2,090
Number of dimes Sue collected= 1,910
Total number of dimes= 2,090+1,910= 4100
Number of stacks= 8
Number of dimes in each stack = Quotient of 4100 ÷8=512

Question 18.
Communicate Mr. Roberts sees a rare 1937 penny. The cost of the penny is $210. If he saves$3 each week, will Mr. Roberts have enough money to buy the penny in one year? Explain.
______

Explanation:
Amount saved in each week= $3 Number of weeks in a year= 52 The total amount saved= 52 x 3=$156
Cost of the penny=$210 Therefore Mr. Roberts cannot buy the penny in one year. ### Page No. 218 Question 20. Which quotients are equal to 20? Mark all that apply. Options: a. 600 ÷ 2 b. 1,200 ÷ 6 c. 180 ÷ 9 d. 140 ÷ 7 e. 500 ÷ 5 Answer: c. 180 ÷ 9 d. 140 ÷ 7 Explanation: Quotient: A. Use 180 counters to represent the 180 dominoes. Then draw 9 circles to represent the divisor. B. Share the counters equally among the 9 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 180 ÷ 9 D. Number of circles are equally filled with 20 counters, therefore, the quotient is 20 Quotient: A. Use 140 counters to represent the 140 dominoes. Then draw 7 circles to represent the divisor. B. Share the counters equally among the 7 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 140 ÷ 7 D. Number of circles are equally filled with 20 counters, therefore, the quotient is 20 Insect Flight True flight is shared only by insects, bats, and birds. Flight in insects varies from the clumsy flight of some beetles to the acrobatic moves of dragonflies. The wings of insects are not moved by muscles attached to the wings. Muscles in the middle part of the body, or the thorax, move the wings. The thorax changes shape as the wings move. Question 21. About how many times do a damselfly’s wings beat in 1 minute? ______ times Answer: 900 Explanation: Total number of wingbeats of Damselfly in 3 minutes= 2,700 Number of wingbeats of Damselfly in 1 minute= 2,700 ÷3=900 Question 22. About how many times do a scorpion fly’s wings beat in 6 minutes? ______ times Answer: 10,000 Explanation: Total number of wingbeats of scorpionfly in 3 minutes=5,000 Number of parts of time-intervals in 6 minutes = 6÷3=2 Number of wingbeats of scorpionfly in 6 minutes= 5,000 x 2 = 10,000 Question 23. In one minute, how many more times do a damselfly’s wings beat than a large white butterfly’s wings? ______ more times Answer: 200 Explanation: Total number of wingbeats of Damselfly in 3 minutes= 2,700 Number of wingbeats of Damselfly in 1 minute= 2,700 ÷3=900 Total number of wingbeats of large white butterfly in 3 minutes= 2,100 Number of wingbeats of large white butterfly in 1 minute= 2,100 ÷3=700 Number of more times the damselfly’s wings beat than a large white butterfly=900-700=200 Question 24. What’s the Question? The answer is about 2,300 times. Type below: ___________ Answer: About how many times do an Aeschind dragonfly’s wings beat in 1 minute? Explanation: Total number of wingbeats of Aeschind dragonfly’s in 3 minutes= 6,900 Number of wingbeats of Aeschind dragonfly’s in 1 minute= 6,900 ÷3=2,300 ### Common Core – Page No. 219 Divide Tens, Hundreds, and Thousands Use basic facts and place value to find the quotient. Question 1. 3,600 ÷ 4 = 900 Think: 3,600 is 36 hundreds. Use the basic fact 36 ÷ 4 = 9. So, 36 hundreds ÷ 4 = 9 hundreds, or 900. Answer: 900 Explanation: STEP 1 Identify the basic fact. 36 ÷ 4 STEP 2 Use place value. 3,600 = 36 hundreds STEP 3 Divide. 36 hundered ÷ 4 = 9 hundreds 3,600 ÷ 4 = 900 Question 2. 240 ÷ 6 = ______ Answer: 40 Explanation: STEP 1 Identify the basic fact. 24 ÷ 6 STEP 2 Use place value. 240 = 24 tens STEP 3 Divide. 24 tens ÷ 6 = 4 tens 240 ÷ 6 = 40 Question 3. 5,400 ÷ 9 = ______ Answer: 600 Explanation: STEP 1 Identify the basic fact. 54 ÷ 9 STEP 2 Use place value. 5,400 = 54 hundreds STEP 3 Divide. 54 hundreds ÷ 9 = 6 hundreds 5,400 ÷ 9 = 600 Question 4. 300 ÷ 5 = ______ Answer: 60 Explanation: STEP 1 Identify the basic fact. 30 ÷ 5 STEP 2 Use place value. 300 = 30 tens STEP 3 Divide. 30 tens ÷ 5 = 60 tens 300 ÷ 5 = 60 Question 5. 4,800 ÷ 6 = ______ Answer: 800 Explanation: STEP 1 Identify the basic fact. 48 ÷ 6 STEP 2 Use place value. 4,800 = 48 hundreds STEP 3 Divide. 48 hundreds ÷ 6 = 80 hundreds 4,800 ÷ 6 = 800 Question 6. 420 ÷ 7 = ______ Answer: 60 Explanation: STEP 1 Identify the basic fact. 42 ÷ 7 STEP 2 Use place value. 420 = 42 tens STEP 3 Divide. 42 tens ÷ 7 = 60 tens 420 ÷ 7 = 60 Question 9. 1,200 ÷ 4 = ______ Answer: 300 Explanation: STEP 1 Identify the basic fact. 12 ÷ 4 STEP 2 Use place value. 1,200 = 12 hundreds STEP 3 Divide. 12 hundreds ÷ 4 = 3 hundreds 1,200 ÷ 4 = 300 Question 10. 360 ÷ 6 = ______ Answer: 60 Explanation: STEP 1 Identify the basic fact. 36 ÷ 6 STEP 2 Use place value. 360 = 36 tens STEP 3 Divide. 36 tens ÷ 6 = 6 tens 360 ÷ 6 = 60 Find the quotient. Question 11. 28 ÷ 4 = ______ 280 ÷ 4 = ______ 2,800 ÷ 4 = ______ Answer: 7, 70, 700 Explanation: Quotient: A. Use 28 counters to represent the 28 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 28 ÷ 4 D. Number of circles are equally filled with 7 counters, therefore, the quotient is 7 STEP 1 Identify the basic fact. 28 ÷ 4 STEP 2 Use place value. 280 = 28 tens STEP 3 Divide. 28 tens ÷ 4 = 7 tens 280 ÷ 4 = 70 STEP 1 Identify the basic fact. 28 ÷ 4 STEP 2 Use place value. 2,800 = 28 hundreds STEP 3 Divide. 28 hundreds ÷ 4 = 7 hundreds 2,800 ÷ 4 = 700 Question 12. 18 ÷ 3 = ______ 180 ÷ 3 = ______ 1,800 ÷ 3 = ______ Answer: 6, 60, 600 Explanation: Quotient: A. Use 18 counters to represent the 18 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 18 ÷ 3 D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6 STEP 1 Identify the basic fact. 18 ÷ 3 STEP 2 Use place value. 180 = 18 tens STEP 3 Divide. 18 tens ÷ 3 = 6 tens 180 ÷ 6 = 60 STEP 1 Identify the basic fact. 18 ÷ 3 STEP 2 Use place value. 1,800 = 18 hundreds STEP 3 Divide. 18 hundreds ÷ 3 = 6 hundreds 1,800 ÷ 3 = 600 Question 13. 45 ÷ 9 = ______ 450 ÷ 9 = ______ 4,500 ÷ 9 = ______ Answer: 5, 50, 500 Explanation: Quotient: A. Use 45 counters to represent the 45 dominoes. Then draw 9 circles to represent the divisor. B. Share the counters equally among the 9 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 45 ÷ 9 D. Number of circles are equally filled with 5 counters, therefore, the quotient is 5 STEP 1 Identify the basic fact. 45 ÷ 9 STEP 2 Use place value. 450 = 45 tens STEP 3 Divide. 45 tens ÷ 9 = 5 tens 450 ÷ 9 = 50 STEP 1 Identify the basic fact. 45 ÷ 9 STEP 2 Use place value. 4,500 = 45 hundreds STEP 3 Divide. 45 hundreds ÷ 9 = 5 hundreds 4,500 ÷ 9 = 500 Problem Solving Question 14. At an assembly, 180 students sit in 9 equal rows. How many students sit in each row? ______ students Answer: 20 Explanation: Total number of students= 180 Number of rows= 9 Number of students in each row= 180 ÷9=20 Question 15. Hilary can read 560 words in 7 minutes. How many words can Hilary read in 1 minute? ______ words Answer: 80 Explanation: Total number of words Hilary can read in 7 minutes = 560 Number of words Hilary can read in 1 minute= 560 ÷ 7= 80 ### Common Core – Page No. 220 Lesson Check Question 1. A baseball player hits a ball 360 feet to the outfield. It takes the ball 4 seconds to travel this distance. How many feet does the ball travel in 1 second? Options: a. 9 feet b. 40 feet c. 90 feet d. 900 feet Answer: c. 90 feet Explanation: The height to which the player hits a ball=360 feet Height to which the ball travels in 1 second= 360÷4= 90 feet Question 2. Sebastian rides his bike 2,000 meters in 5 minutes. How many meters does he bike in 1 minute? Options: a. 4 meters b. 40 meters c. 50 meters d. 400 meters Answer: d. 400 meters Explanation: Total number of meters travelled in 5 minutes= 2,000 Number of meters travelled in 1 minute= 2,000÷5= 400 Spiral Review Question 3. A full container of juice holds 63 ounces. How many 7-ounce servings of juice are in a full container? Options: a. 1 b. 8 c. 9 d. 10 Answer: c. 9 Explanation: A full container of juice holds= 63 ounces Quantity of servings of juice in one glass=7 ounce Number of servings of the juice are= 63÷7=9 Question 4. Paolo pays$244 for 5 identical calculators. Which is the best estimate of how much Paolo pays for one calculator?
Options:
a. $40 b.$50
c. $60 d.$245

Answer: b. $50 Explanation: Amount Paolo pays for the identical calculators =$244
Number of identical calculators=5
The best-estimated value of each identical calculator=$244 ÷ 5is approximately$50

Question 5.
A football team paid $28 per jersey. They bought 16 jerseys. How much money did the team spend on jerseys? Options: a.$44
b. $196 c.$408
d. $448 Answer: d.$448

Explanation:
Cost of each jersey=$28 Number of jerseys= 16 Total cost of the jerseys=$28 x 16= $448 Question 6. Suzanne bought 50 apples at the apple orchard. She bought 4 times as many red apples as green apples. How many more red apples than green apples did Suzanne buy? Options: a. 10 b. 25 c. 30 d. 40 Answer: d. 40 Explanation: Let the number of green apples be x and the number of red apples be 4x 4x + x = 50 x = 50 ÷ 5= 10 Number of red balls = 4x = 4 x 10 = 40 ### Page No. 222 Question 1. Estimate. 1,718 ÷ 4 Think: What number close to 1,718 is easy to divide by 4? ______ is close to 1,718. What basic fact can you use? ______ ÷ 4 ______ is close to 1,718. What basic fact can you use? ______ ÷ 4 Choose 1,600 because __________________________________. 16 ÷ 4 = ______ 1,600 ÷ ______ = ______ 1,718 ÷ 4 is about ______ Type below: _________ Answer: Explanation: What number close to 1,718 is easy to divide by 4? 1,600 is close to 1,718. What basic fact can you use? 1,600 ÷ 4 Choose 1,600 because it is close to 1,718 and can easily be divided by 4. 16 ÷ 4 = 4 1,600 ÷ 4 = 400 1,600 ÷ 4 is about 400 Use compatible numbers to estimate the quotient. Question 2. 455 ÷ 9 ______ Answer: 50 Explanation: What number close to 455 is easy to divide by 9? 450 is close to 455. What basic fact can you use? 450 ÷ 9 Choose 450 because it is close to 455 and can easily be divided by 9. 45 ÷ 9 = 5 450 ÷ 9 = 50 455 ÷ 9 is about 50 Question 3. 1,509 ÷ 3 ______ Answer: 500 Explanation: What number close to 1,509 is easy to divide by 3? 1,500 is close to 1,509. What basic fact can you use? 1,500 ÷ 3 Choose 1,500 because it is close to 1,509 and can easily be divided by 3. 15 ÷ 3 = 5 1,500 ÷ 3 = 500 1,509 ÷ 3 is about 500 Question 4. 176 ÷ 8 ______ Answer: Explanation: What number close to 176 is easy to divide by 8? 160 is close to 176. What basic fact can you use? 160 ÷ 8 Choose 160 because it is close to 176 and can easily be divided by 8. 16 ÷ 8 = 2 160 ÷ 8 = 20 176 ÷ 8 is about 20 Question 5. 2,795 ÷ 7 ______ Answer: 400 Explanation: What number close to 2,795 is easy to divide by 7? 2,800 is close to 2,795. What basic fact can you use? 2,800 ÷ 7 Choose 2,800 because it is close to 2,795 and can easily be divided by 7. 28 ÷ 7 = 4 2,800 ÷ 7 = 400 2,795 ÷ 7 is about 400 Use compatible numbers to find two estimates that the quotient is between. Question 6. 5,321 ÷ 6 ______ and ______ Answer: 900 Explanation: What number close to 5,321 is easy to divide by 6? 5,400 is close to 5,321. What basic fact can you use? 5,400 ÷ 6 Choose 5,400 because it is close to 5,321 and can easily be divided by 6. 54 ÷ 6 = 9 5,400 ÷ 6 = 900 5,321 ÷ 6 is about 900 Question 7. 1,765 ÷ 6 ______ and ______ Answer: 300 Explanation: What number close to 1,765 is easy to divide by 6? 1,800 is close to 1,765. What basic fact can you use? 1,800 ÷ 6 Choose 1,800 because it is close to 1,765 and can easily be divided by 6. 18 ÷ 6 = 3 1,800 ÷ 6 = 300 1,765 ÷ 6 is about 300 Question 8. 1,189 ÷ 3 ______ and ______ Answer: 400 Explanation: What number close to 1,189 is easy to divide by 3? 1,200 is close to 1,189. What basic fact can you use? 1,200 ÷ 3 Choose 1,200 because it is close to 1,189 and can easily be divided by 3. 12 ÷ 3 = 4 1,200 ÷ 3 = 400 1,189 ÷ 3 is about 400 Question 9. 2,110 ÷ 4 ______ and ______ Answer: 500 Explanation: What number close to 2,110 is easy to divide by 4? 2,000 is close to 2,110. What basic fact can you use? 2,000 ÷ 4 Choose 2,000 because it is close to 2,110 and can easily be divided by 4. 20 ÷ 4 = 5 2,000 ÷ 4 = 500 2,110 ÷ 4 is about 500 Reason Abstractly Algebra Estimate to compare. Write <, >, or =. Question 10. 613 ÷ 3 ______ 581 ÷ 2 Answer: 613 ÷ 3 < 581 ÷ 2 Explanation: What number close to 613 is easy to divide by 3? 600 is close to 613. What basic fact can you use? 600 ÷ 3 Choose 600 because it is close to 613 and can easily be divided by 3. 6 ÷ 3 = 2 600 ÷ 3 = 200 613 ÷ 3 is about 200 What number close to 581 is easy to divide by 2? 580 is close to 581. What basic fact can you use? 580 ÷ 2 Choose 580 because it is close to 581 and can easily be divided by 2. 58 ÷ 2 = 29 580 ÷ 2 = 290 581 ÷ 2 is about 290 Question 11. 364 ÷ 4 ______ 117 ÷ 6 Answer: 364 ÷ 4 > 117 ÷ 6 Explanation: What number close to 364 is easy to divide by 4? 360 is close to 364. What basic fact can you use? 360 ÷ 4 Choose 360 because it is close to 364 and can easily be divided by 4. 36 ÷ 4 = 9 360 ÷ 4 = 90 364 ÷ 4 is about 90 What number close to 117 is easy to divide by 6? 120 is close to 117. What basic fact can you use? 120 ÷ 6 Choose 120 because it is close to 117 and can easily be divided by 6. 12 ÷ 6 = 2 120 ÷ 6 = 20 117 ÷ 6 is about 20 Question 12. 2,718 ÷ 8 ______ 963 ÷ 2 Answer: 2,718 ÷ 8 < 963 ÷ 2 Explanation: What number close to 2,718 is easy to divide by 8? 2,400 is close to 2,718. What basic fact can you use? 2,400 ÷ 8 Choose 2,400 because it is close to 2,718 and can easily be divided by 8. 24 ÷ 8 = 3 2,400 ÷ 8 = 300 2,718 ÷ 8 is about 300 What number close to 963 is easy to divide by 2? 960 is close to 963. What basic fact can you use? 960 ÷ 2 Choose 960 because it is close to 963 and can easily be divided by 2. 96 ÷ 2 = 48 960 ÷ 2 = 480 963 ÷ 2 is about 480 ### Page No. 223 Use the table for 15–17. Question 15. About how many times does a chicken’s heart beat in 1 minute? about ______ times Answer: 275 Explanation: Number of times the chicken’s heartbeats in 5 minutes= 1,375 Number of times the chicken’s heartbeats in 1 minute= 1,375÷ 5= 275 Question 16. About how many times does a cow’s heart beat in 2 minutes? about ______ times Answer: 130 Explanation: Number of times the cow’s heartbeats in 5 minutes= 325 Number of times the cow’s heartbeats in 1 minute= 325÷5=65 Number of times the cow’s heartbeats in 2 minutes= 65 x 2=130 Question 17. Use Reasoning About how many times faster does a cow’s heart beat than a whale’s? about ______ times Answer: nearly 11 times Explanation: Number of times the cow’s heartbeats in 5 minutes= 325 Number of times the cow’s heartbeats in 1 minute= 325÷5=65 Number of times the whale’s heartbeats in 5 minutes= 31 Number of times the whale’s heartbeats in 1 minute= 31÷5=6.2= rounding to nearest whole number 6 (approx) Number of more times the cow’s heartbeats compared to whale’s=65÷6=10.8 times=rounding to a nearest whole number 11(approx) Question 18. Martha had 154 stamps and her sister had 248 stamps. They combined their collections and put the stamps in an album. If they want to put 8 stamps on each page, about how many pages would they need? about ______ times Answer: 50.25 pages Explanation: Number of stamps Martha has= 154 Number of stamps Martha’s sister has= 248 The total number of stamps they have = 154 +248 = 402 Number of stamps on each page= 8 Number of pages= 402÷8= 50.25 pages= 51 (approx) ### Page No. 224 Question 21. Cause and Effect The reading skill cause and effect can help you understand how one detail in a problem is related to another detail. Chet wants to buy a new bike that costs$276. Chet mows his neighbor’s lawn for $15 each week. Since Chet does not have money saved, he needs to decide which layaway plan he can afford to buy the new bike. Which plan should Chet choose? 3-month layaway:$276 ÷ 3
Estimate.
$270 ÷ 3 ______ 6-month layaway:$276 ÷ 6
Estimate.
$300 ÷ 6 _____ Chet earns$15 each week. Since there are usually 4 weeks in a month, multiply to see which payment he can afford.
$15 × 4 = _______ So, Chet can afford the ______ layaway plan. Type below: ___________ Answer: Chet can afford the 3-month layaway plan. Explanation: What number close to$276  is easy to divide by 3?
$270 is close to$276. What basic fact can you use?
$270 ÷ 3 Choose 270 because it is close to 276 and can easily be divided by 3. 27 ÷ 3 = 9 270 ÷ 3 = 90$276 ÷ 3 is about 90

Use estimation to solve.

Question 21.
Sofia wants to buy a new bike that costs $214. Sofia helps her grandmother with chores each week for$18. Estimate to find which layaway plan Sofia should choose and why.
Type below:
___________

Explanation:
What number close to $214 is easy to divide by 3?$215 is close to $214. What basic fact can you use?$215 ÷ 3
Choose 215 because it is close to 214 and can easily be divided by 3.
215 ÷ 3 = 71.6=72 (approx)
$214 ÷ 3 is about 72 Question 22. Describe a situation when you have used cause and effect to help you solve a math problem. Type below: ___________ Answer: To buy a bike Explanation: 3-month layaway:$276 ÷ 3
Estimate.
$270 ÷ 3 ______ 6-month layaway:$276 ÷ 6
Estimate.
$300 ÷ 6 _____ Chet earns$15 each week. Since there are usually 4 weeks in a month, multiply to see which payment he can afford.
$15 × 4 = _______ So, Chet can afford the ______ layaway plan. The above is a profit gaining plan to buy a bike. ### Common Core – Page No. 224 Estimate Quotients Using Compatible Numbers Use compatible numbers to estimate the quotient. Question 1. 389 ÷ 4 400 ÷ 4 = 100 Answer: 100 Explanation: What number close to 389 is easy to divide by 4? 400 is close to 389. What basic fact can you use? 400 ÷ 4 Choose 400 because it is close to 389 and can easily be divided by 4. 40 ÷ 4 = 10 400 ÷ 4 = 100 389 ÷ 4 is about 100 Question 2. 358 ÷ 3 _____ ÷ 3 = _____ Answer: 120 Explanation: What number close to 358 is easy to divide by 3? 360 is close to 358. What basic fact can you use? 360 ÷ 3 Choose 360 because it is close to 358 and can easily be divided by 3. 36 ÷3 = 12 360 ÷ 3 =120 358 ÷ 3 is about 120 Question 3. 784 ÷ 8 _____ ÷ 8 = _____ Answer: 100 Explanation: What number close to 784 is easy to divide by 8? 800 is close to 784. What basic fact can you use? 800 ÷ 8 Choose 800 because it is close to 784 and can easily be divided by 8. 80 ÷ 8 = 10 800 ÷ 8 = 100 784 ÷ 8 is about 100 Question 4. 179 ÷ 9 _____ ÷ 9 = _____ Answer: 20 Explanation: What number close to 179 is easy to divide by 9? 180 is close to 179. What basic fact can you use? 180 ÷ 9 Choose 180 because it is close to 179 and can easily be divided by 9. 18 ÷ 9 = 2 180 ÷ 9 = 20 179 ÷ 9 is about 20 Question 5. 315 ÷ 8 _____ ÷ 8 = _____ Answer: 40 Explanation: What number close to 315 is easy to divide by 8? 320 is close to 315. What basic fact can you use? 320 ÷ 8 Choose 320 because it is close to 315 and can easily be divided by 8. 32 ÷ 8 = 4 320 ÷ 8 =40 315 ÷ 8 is about 40 Question 6. 2,116 ÷ 7 _____ ÷ 7 = _____ Answer: 300 Explanation: What number close to 2,116 is easy to divide by 7? 2,100 is close to 2,116. What basic fact can you use? 2,100 ÷ 7 Choose 2,100 because it is close to 2,116 and can easily be divided by 7. 21 ÷ 7= 3 2,100 ÷ 7 = 300 2,116 ÷ 7 is about 300 Question 7. 4,156 ÷ 7 _____ ÷ 7 = _____ Answer: 600 Explanation: What number close to 4,156 is easy to divide by 7? 4,200 is close to 4,156. What basic fact can you use? 4,200 ÷7 Choose 4,200 because it is close to 4,156 and can easily be divided by 7. 42 ÷ 7 = 6 4,200 ÷ 7 = 600 4,156 ÷ 7 is about 600 Question 8. 474 ÷ 9 _____ ÷ 9 = _____ Answer: 50 Explanation: What number close to 474 is easy to divide by 9? 450 is close to 474. What basic fact can you use? 450 ÷ 9 Choose 450 because it is close to 474 and can easily be divided by 9. 45 ÷ 9 = 5 450 ÷ 9 = 50 474 ÷ 9 is about 50 Use compatible numbers to find two estimates that the quotient is between. Question 9. 1,624 ÷ 3 _____ ÷ 3 = _____ _____ ÷ 3 = _____ Answer: The quotient is between 500 and 600 Explanation: What number close to 1,624 is easy to divide by 3? 1,500 is close to 1,624. What basic fact can you use? 1,500 ÷ 3 Choose 1,500 because it is close to 1,624 and can easily be divided by 3. 15 ÷ 3 = 5 1,500 ÷ 3 = 500 1,624 ÷ 3 is about 500 What number close to 1,624 is easy to divide by 3? 1,800 is close to 1,624. What basic fact can you use? 1,800 ÷ 3 Choose 1,800 because it is close to 1,624 and can easily be divided by 3. 18 ÷ 3 = 6 1,800 ÷ 3 = 600 1,624 ÷ 3 is about 600 Question 10. 2,593 ÷ 6 _____ ÷ 6 = _____ _____ ÷ 6 = _____ Answer: The quotient is between 400 and 500 Explanation: What number close to 2,593 is easy to divide by 6? 2,400 is close to 2,593. What basic fact can you use? 2,400 ÷ 6 Choose 2,400 because it is close to 2,593 and can easily be divided by 6. 24 ÷ 6 = 4 2,400 ÷ 6 = 400 2,593 ÷ 6 is about 400 What number close to 2,593 is easy to divide by 6? 3,000 is close to 2,593. What basic fact can you use? 3000 ÷ 6 Choose 3,000 because it is close to 2,593 and can easily be divided by 6. 30 ÷ 6 = 5 3,000 ÷ 6 = 500 2,593 ÷ 6 is about 500 Question 11. 1,045 ÷ 2 _____ ÷ 2 = _____ _____ ÷ 2 = _____ Answer: The quotient is between 520 and 525 Explanation: What number close to 1,045 is easy to divide by 2? 1,040 is close to 1,045. What basic fact can you use? 1,040 ÷ 2 Choose 1,040 because it is close to 1,045 and can easily be divided by 2. 1,04 ÷ 2 = 52 1,040 ÷ 2 = 520 1,045 ÷ 2 is about 520 What number close to 1,045 is easy to divide by 2? 1,050 is close to 1,045. What basic fact can you use? 1,050 ÷ 2 Choose 1,050 because it is close to 1,045 and can easily be divided by 2. 1,050 ÷ 2 = 525 1,045 ÷ 2 is about 525 Question 12. 1,754 ÷ 9 _____ ÷ 9 = _____ _____ ÷ 9 = _____ Answer: The quotient is between 195 and 200 Explanation: What number close to 1,754 is easy to divide by 9? 1,755 is close to 1,754. What basic fact can you use? 1,755 ÷ 9 Choose 1,755 because it is close to 1,754 and can easily be divided by 9. 1,755 ÷ 9 = 195 1,754 ÷ 9 is about 195 What number close to 1,754 is easy to divide by 9? 1,800 is close to 1,754. What basic fact can you use? 1,800 ÷ 9 Choose 1,800 because it is close to 1,754 and can easily be divided by 9. 18 ÷ 9 = 2 1,800 ÷ 9 = 200 1,754 ÷ 9 is about 200 Question 13. 2,363 ÷ 8 _____ ÷ 8 = _____ _____ ÷ 8 = _____ Answer: The quotient is between 295 and 300 Explanation: What number close to 2,363 is easy to divide by 8? 2,360 is close to 2,363. What basic fact can you use? 2,360 ÷ 8 Choose 2,360 because it is close to 2,363 and can easily be divided by 8. 2,360 ÷ 8 = 295 2,363 ÷ 8 is about 295 What number close to 2,363 is easy to divide by 8? 2,400 is close to 2,363. What basic fact can you use? 2,400 ÷ 8 Choose 2,400 because it is close to 2,363 and can easily be divided by 8. 24 ÷ 8 = 3 2,400 ÷ 8= 300 2,363 ÷ 8 is about 300 Question 14. 1,649 ÷ 5 _____ ÷ 5 = _____ _____ ÷ 5 = _____ Answer: The quotient is between 329 and 330 Explanation: What number close to 1,649 is easy to divide by 5? 1,645 is close to 1,649. What basic fact can you use? 1,645 ÷ 5 Choose 1,645 because it is close to 1,649 and can easily be divided by 5. 1,645 ÷ 5 = 329 1,649 ÷ 5 is about 329 What number close to 1,650 is easy to divide by 5? 1,650 is close to 1,649. What basic fact can you use? 1,650 ÷ 5 Choose 1,650 because it is close to 1,649 and can easily be divided by 5. 1,650 ÷ 5 = 330 1,649 ÷ 5 is about 330 Question 15. 5,535 ÷ 7 _____ ÷ 7 = _____ _____ ÷ 7 = _____ Answer: The quotient is between 790 and 791 Explanation: What number close to 5,535 is easy to divide by 7? 5,530 is close to 5,535. What basic fact can you use? 5,530 ÷ 7 Choose 5,530 because it is close to 5,535 and can easily be divided by 7. 553 ÷ 7 = 79 5,530 ÷ 7 = 790 5,535 ÷ 7 is about 790 What number close to 5,535 is easy to divide by 7? 5,537 is close to 5,535. What basic fact can you use? 5,537 ÷ 7 Choose 5,537 because it is close to 5,535 and can easily be divided by 7. 553 ÷ 7 = 79 5,537 ÷ 7 = 791 5,535 ÷ 7 is about 791 Question 16. 3,640 ÷ 6 _____ ÷ 6 = _____ _____ ÷ 6 = _____ Answer: The quotient is between 606 and 607 Explanation: What number close to 3,640 is easy to divide by 6? 3,636 is close to 3,640. What basic fact can you use? 3,636 ÷ 6 Choose 3,636 because it is close to 3,640 and can easily be divided by 6. 36 ÷ 6 = 6 3,636 ÷ 6 = 606 3,640 ÷ 6 is about 606 What number close to 3,640 is easy to divide by 6? 3,642 is close to 3,640. What basic fact can you use? 3,642 ÷ 6 Choose 3,642 because it is close to 3,640 and can easily be divided by 6. 3,642 ÷ 6 = 607 3,640 ÷ 6 is about 607 Problem Solving Question 17. A CD store sold 3,467 CDs in 7 days. About the same number of CDs were sold each day. About how many CDs did the store sell each day? about _____ CDs Answer: 495(approx) Explanation: Total number of CDs in the store= 3,467 Number of days= 7 Number of CDs sold on one day= 3,467 ÷ 7=495(approx) Question 18. Marcus has 731 books. He puts about the same number of books on each of 9 shelves in his a bookcase. About how many books are on each shelf? about _____ books Answer: 81 books(approx) Explanation: Total number of books Marcus has= 731 Number of shelves= 9 Number of books on each shelf= 731÷9= 81 (approx) ### Common Core – Page No. 226 Lesson Check Question 1. Jamal is planting seeds for a garden nursery. He plants 9 seeds in each container. If Jamal has 296 seeds to plant, how many containers will he use? Options: a. about 20 b. about 30 c. about 200 d. about 300 Answer: b. about 30 Explanation: Total number of seeds Jamal has= 296 Number of seeds placed in each container= 9 Number of containers Jamal used= 296÷9= 32.8=33 (approx) Therefore, the number of containers used is about 30 Question 2. Winona purchased a set of vintage beads. There are 2,140 beads in the set. If she uses the beads to make bracelets that have 7 beads each, how many bracelets can she make? Options: a. about 30 b. about 140 c. about 300 d. about 14,000 Answer: c. about 300 Explanation: Total number of beads Winona has= 2,140 Number of beads in each bracelet= 7 Number of bracelets made= 2,140÷7=305.7=306(approx) Therefore, the number of bracelets made are about 30 Spiral Review Question 3. A train traveled 360 miles in 6 hours. How many miles per hour did the train travel? Options: a. 60 miles per hour b. 66 miles per hour c. 70 miles per hour d. 600 miles per hour Answer: a. 60 miles per hour Explanation: Total number of miles travelled by the train= 360 Time taken by the train to cover 360 miles= 6 hours Number of miles travelled in each hour= 360÷6=60 miles Question 4. An orchard has 12 rows of pear trees. Each row has 15 pear trees. How many pear trees are there in the orchard? Options: a. 170 b. 180 c. 185 d. 190 Answer: b. 180 Explanation: Number of rows of pear trees in an orchard= 12 Number of pear trees in each row=15 Total number of pear trees in the orchard= 12 x 15=180 Question 5. Megan rounded 366,458 to 370,000. To which place did Megan round the number? Options: a. hundred thousand b. ten thousand c. thousands d. hundreds Answer: b. ten thousand Explanation: The given number is 366,458, the ten thousand place digit has 6 which while rounding off should be changed to the next consecutive number and the digits in the other places should be written as zeroes. Question 6. Mr. Jessup, an airline pilot, flies 1,350 miles a day. How many miles will he fly in 8 days? Options: a. 1,358 miles b. 8,400 miles c. 10,800 miles d. 13,508 miles Answer: c. 10,800 miles Explanation: Number of miles flew by Mr.Jessup in one day= 1,350 miles Number of days=8 Total number of miles flew by Mr.Jessup in 8 days= 1,350 x 8= 10,800 miles ### Page No. 229 Model the division on the grid. Question 1. 26 ÷ 2 = (□ ÷ 2) + (□ ÷ 2) = □ + □ = □ Type below: _________ Answer: 26 ÷ 2 = (20 ÷ 2) + (6 ÷ 2) = 10 + 3 = 13 Explanation: A. Outline a rectangle on a grid to model 26 ÷ 2. Shade columns of 2 until you have 26 squares. How many groups of 2 can you make? B. Think of 26 as 20 + 6. Break apart the model into two rectangles to show (20 + 6 ) ÷ 2. Label and shade the smaller rectangles. Use two different colours. C. Each rectangle models a division. 26 ÷ 2 = (20÷ 2 ) + (6÷ 2) = 10+ 3 = 13 Question 2. 45 ÷ 3 = (□ ÷ 3) + (□ ÷ 3) = □ + □ = □ Type below: _________ Answer: 45 ÷ 3 = (15 ÷ 3) + (30 ÷ 3) = 5 + 10 = 15 Explanation: A. Outline a rectangle on a grid to model 45 ÷ 3. Shade columns of 3 until you have 45 squares. How many groups of 3 can you make? _ B. Think of 45 as 15 + 30. Break apart the model into two rectangles to show (15 + 30 ) ÷ 3. Label and shade the smaller rectangles. Use two different colours. C. Each rectangle models a division. 45 ÷ 3 = (15÷ 3 ) + (30÷ 3 ) = 5 + 10 = 15 Find the quotient. Question 3. 82 ÷ 2 = (□ ÷ 2) + (□ ÷ 2) = □ + □ = □ ______ Answer: 82 ÷ 2 = (80 ÷ 2) + ( 2÷ 2) = 40 + 1 = 41 Explanation: A. Outline a rectangle on a grid to model 82 ÷ 2. Shade columns of 2 until you have 80 squares. How many groups of 2 can you make? B. Think of 82 as 80 + 2. Break apart the model into two rectangles to show (80 + 2 ) ÷ 2. Label and shade the smaller rectangles. Use two different colors. C. Each rectangle models a division. 82 ÷ 2 = (80 ÷ 2 ) + (2÷ 2) = 40 + 1 = 41 Question 4. 208 ÷ 4 = (□ ÷ 4) + (□ ÷ 4) = □ + □ = □ ______ Answer: 208 ÷ 4 = (200 ÷ 4) + (8 ÷ 4) = 50 + 4 = 54 Explanation: A. Outline another model to show 208 ÷ 4. How many groups of 4 can you make? B. Think of 208 as 200 + 8. Break apart the model, label, and shade to show two divisions. 208 ÷ 4 = (200 ÷ 4 ) + (8 ÷ 4 ) = 50 + 4 = 54 Use base-ten blocks to model the quotient. Then record the quotient. Question 5. 88 ÷ 4 = ______ Answer: 22 Explanation: A. Outline another model to show 88 ÷ 4. How many groups of 4 can you make? B. Think of 88 as 80 + 8. Break apart the model, label, and shade to show two divisions. 88 ÷ 4 = (80 ÷ 4 ) + (8 ÷ 4 ) = 40 + 4 = 44 Question 6. 36 ÷ 3 = ______ Answer: 12 Explanation: A. Outline a rectangle on a grid to model 36 ÷ 3. Shade columns of 3 until you have 36 squares. How many groups of 3 can you make? _ B. Think of 36 as 6 + 30. Break apart the model into two rectangles to show (6 + 30 ) ÷ 3. Label and shade the smaller rectangles. Use two different colours. C. Each rectangle models a division. 36 ÷ 3 = (30÷ 3 ) + (6÷ 3 ) = 10 + 2 = 12 Question 7. 186 ÷ 6 = ______ Answer: 31 Explanation: A. Outline a rectangle on a grid to model 186 ÷ 6. Shade columns of 18 until you have 180 squares. How many groups of 6 can you make? _ B. Think of 186 as 6 + 180. Break apart the model into two rectangles to show (6 + 180 ) ÷ 6. Label and shade the smaller rectangles. Use two different colours. C. Each rectangle models a division. 186 ÷ 6 = (180÷ 6 ) + (6÷ 6 ) = 30 + 1 = 31 Question 8. Explain how you can model finding quotients using the Distributive Property. Type below: _________ Answer: We can use the Distributive Property to break apart numbers to make them easier to divide. Explanation: 50 The Distributive Property of division says that dividing a sum by a number is the same as dividing each addend by the number and then adding the quotients. ### Page No. 230 Question 10. Christelle went to a gift shop. The shop sells candles in a variety of sizes and colors. The picture shows a display of candles. Write a problem that can be solved using the picture. Pose a problem. Solve your problem Answer: Question: How many candles are there in the gift shop? Explanation: Count the number of candles in the rows and columns and then multiply them, by this we can find out the total number of candles in the gift shop. Describe how you could change the problem by changing the number of rows of candles. Then solve the problem. Type below: _________ Answer: There will be no change in the solution by changing the number of rows of candles. Explanation: By changing the number of rows of candles the number of columns increases but there will be no change in the total number of candles. Question 11. For 11a–11d, choose Yes or No to indicate if the expression shows a way to break apart the dividend to find the quotient 147 ÷ 7. a. (135 ÷ 7) + (10 ÷ 7) i. yes ii. no Answer: ii. no Explanation: Because 137+10 is not equal to 147 Question 11. b. (147 ÷ 3) + (147 ÷ 4) i. yes ii. no Answer: ii. no Explanation: Because according to the distributive property we need to divide the dividend into two parts, but not the divisor. Question 11. c. (140 ÷ 7) + (7 ÷ 7) i. yes ii. no Answer: i. yes Explanation: 147 ÷ 7 STEP1 Find the nearest estimates of the number 147 STEP2 We can break the number 147 into 140 + 7 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (140 ÷ 7) + (7 ÷ 7) STEP5 Add quotients of the above 20 +1= 21 Question 11. d. (70 ÷ 7) + (77 ÷ 7) i. yes ii. no Answer: i. yes Explanation: 147 ÷ 7 STEP1 Find the nearest estimates of the number 147 STEP2 We can break the number 147 into 70 + 77 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (70 ÷ 7) + (77 ÷ 7) STEP5 Add quotients of the above 10 +11= 21 ### Common Core – Page No. 231 Division and the Distributive Property Find the quotient. Question 1. 54 ÷ 3 = (30 ÷ 3) + (24 ÷ 3) = 10 + 8 = 18 Answer: 18 Explanation: 54 ÷ 3 STEP1 Find the nearest estimates of the number 54 STEP2 We can break the number 54 into 30 + 24 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (30 ÷ 3) + (24÷ 3) STEP5 Add quotients of the above 10 +8= 18 Question 2. 81 ÷ 3 = ______ Answer: 27 Explanation: 81 ÷ 3 STEP1 Find the nearest estimates of the number 81 STEP2 We can break the number 81 into 21 + 60 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (60 ÷ 3) + (21 ÷ 3) STEP5 Add quotients of the above 20 +7= 27 Question 3. 232 ÷ 4 = ______ Answer: 58 Explanation: 232 ÷ 4 STEP1 Find the nearest estimates of the number 232 STEP2 We can break the number 232 into 200 + 32 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (200 ÷ 4) + (32 ÷ 4) STEP5 Add quotients of the above 50 +8= 58 Question 4. 305 ÷ 5 = ______ Answer: 61 Explanation: 305 ÷ 5 STEP1 Find the nearest estimates of the number 305 STEP2 We can break the number 305 into 300 + 5 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (300 ÷ 5) + (5 ÷ 5) STEP5 Add quotients of the above 60 +1= 61 Question 5. 246 ÷ 6 = ______ Answer: 41 Explanation: 246 ÷ 6 STEP1 Find the nearest estimates of the number 246 STEP2 We can break the number 246 into 240 + 6 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (240 ÷ 6) + (6 ÷ 6) STEP5 Add quotients of the above 40 +1= 41 Question 6. 69 ÷ 3 = ______ Answer: 23 Explanation: 69 ÷ 3 STEP1 Find the nearest estimates of the number 69 STEP2 We can break the number 69 into 60 + 9 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (60 ÷ 3) + (9 ÷ 3) STEP5 Add quotients of the above 20 +3= 23 Question 7. 477 ÷ 9 = ______ Answer: 53 Explanation: 477 ÷ 9 STEP1 Find the nearest estimates of the number 477 STEP2 We can break the number 477 into 450 + 27 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (450 ÷ 9) + (27 ÷ 9) STEP5 Add quotients of the above 50 +3= 53 Question 8. 224 ÷ 7 = ______ Answer: 32 Explanation: 224 ÷ 7 STEP1 Find the nearest estimates of the number 224 STEP2 We can break the number 224 into 210 + 14 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (210 ÷ 7) + (14 ÷ 7) STEP5 Add quotients of the above 30 +2= 32 Question 9. 72 ÷ 4 = ______ Answer: 18 Explanation: 72 ÷ 4 STEP1 Find the nearest estimates of the number 72 STEP2 We can break the number 72 into 40 + 32 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (40 ÷ 4) + (32 ÷ 4) STEP5 Add quotients of the above 10 +8= 18 Question 10. 315 ÷ 3 = ______ Answer: 105 Explanation: 315 ÷ 3 STEP1 Find the nearest estimates of the number 315 STEP2 We can break the number 315 into 300 + 15 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (300 ÷ 3) + (15 ÷3) STEP5 Add quotients of the above 100 +5= 105 Problem Solving Question 11. Cecily picked 219 apples. She divided the apples equally into 3 baskets. How many apples are in each basket? ______ apples Answer: 73 apples Explanation: The total number of apples Cecily picked= 219 apples Number of parts into which she wanted to divide the apples= 3 Number of apples in each part = Quotient of 147 ÷ 7 STEP1 Find the nearest estimates of the number 219 STEP2 We can break the number 219 into 210 + 9 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (210 ÷ 3) + (9 ÷ 3) STEP5 Add quotients of the above 70 +3= 73 Question 12. Jordan has 260 basketball cards. He divides them into 4 equal groups. How many cards are in each group? ______ cards Answer: 65 cards Explanation: The total number of basketball cards Jordan has= 260 basketball cards Number of parts into which he wanted to divide the cards= 4 Number of apples in each part = Quotient of 260 ÷ 4 STEP1 Find the nearest estimates of the number 260 STEP2 We can break the number 260 into 240 + 20 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (240 ÷ 4) + (20 ÷ 4) STEP5 Add quotients of the above 60 +5= 65 Question 13. The Wilsons drove 324 miles in 6 hours. If they drove the same number of miles each hour, how many miles did they drive in 1 hour? ______ miles Answer: 54 miles Explanation: The total number of miles drove by Wilson= 324 miles Number of hours he drove = 6 Number of miles drove in each hour = Quotient of 324 ÷ 6 STEP1 Find the nearest estimates of the number 324 STEP2 We can break the number 324 into 300 + 24 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (300 ÷ 6) + (24 ÷ 6) STEP5 Add quotients of the above 50 +4= 54 Question 14. Phil has 189 stamps to put into his stamp album. He puts the same number of stamps on each of 9 pages. How many stamps does Phil put on each page? ______ stamps Answer: 21 stamps Explanation: The total number of stamps Phil has= 189 stamps Number of pages= 9 Number of stamps put on each page = Quotient of 189 ÷ 9 STEP1 Find the nearest estimates of the number 189 STEP2 We can break the number 189 into 180 + 9 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (180 ÷ 9) + (9 ÷ 9) STEP5 Add quotients of the above 20 +1= 21 ### Common Core – Page No. 232 Lesson Check Question 1. A landscaping company planted 176 trees in 8 equal rows in the new park. How many trees did the company plant in each row? Options: a. 18 b. 20 c. 22 d. 24 Answer: c. 22 Explanation: The total number of trees in the landscaping= 176 trees Number of rows= 8 Number of trees in each row = Quotient of 176 ÷ 8 STEP1 Find the nearest estimates of the number 176 STEP2 We can break the number 176 into 160 + 16 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (160 ÷ 8) + (16 ÷ 8) STEP5 Add quotients of the above 20 +2= 22 Question 2. Arnold can do 65 pushups in 5 minutes. How many pushups can he do in 1 minute? Options: a. 11 b. 13 c. 15 d. 17 Answer: b. 13 Explanation: The total number of pushups done by Arnold = 65 Number of minutes spent on pushups= 5 Number of pushups done in each minute = Quotient of 65 ÷ 5 STEP1 Find the nearest estimates of the number 65 STEP2 We can break the number 65 into 60 + 5 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (60 ÷ 5) + (5 ÷ 5) STEP5 Add quotients of the above 12 +1= 13 Spiral Review Question 3. Last Saturday, there were 1,486 people at the Cineplex. There were about the same number of people in each of the 6 theaters. Which is the best estimate of the number of people in each theater? Options: a. between 20 and 30 b. between 80 and 90 c. between 100 and 200 d. between 200 and 300 Answer: d. between 200 and 300 Explanation: Total number of people at the Cineplex= 1,486 people Number of theatres = 6 Number of people at each theatre= estimate of the number of people 1,486 ÷ 6 What number close to 1,486 is easy to divide by 6? 1,488 is close to 1,486. What basic fact can you use? 1,488 ÷ 6 Choose 1,488 because it is close to 1,486 and can easily be divided by 6. 1,488 ÷ 6 = 248 1,486 ÷ 6 is about 248 What number close to 1,486 is easy to divide by 6? 1,482 is close to 1,486 . What basic fact can you use? 1,482 ÷ 6 Choose 1,482 because it is close to 1,486 and can easily be divided by 6. 1,482 ÷ 6 = 247 1,486 ÷ 6 is about 247 Question 4. Nancy walked 50 minutes each day for 4 days last week. Gillian walked 35 minutes each day for 6 days last week. Which statement is true? Options: a. Gillian walked 10 minutes more than Nancy. b. Gillian walked 20 minutes more than Nancy. c. Nancy walked 10 minutes more than Gillian. d. Nancy walked 15 minutes more than Gillian. Answer: d. Nancy walked 15 minutes more than Gillian. Explanation: Time walked by Nancy= 50 minutes Time walked by Gillian= 35 minutes Nancy walked more time compared to Gillian 50-35=15 minutes Therefore, Nancy walked 15 minutes more than Gillian. Question 5. Three boys share 28 toy cars equally. Which best describes how the cars are shared? Options: a. Each gets 3 cars with 1 left over. b. Each gets 8 cars with 2 left over. c. Each gets 9 cars with 1 left over. d. Each gets 10 cars with 2 left over. Answer: c. Each gets 9 cars with 1 left over. Explanation: Total number of toys three boys have= 28 Number of toys each boy got= 28 ÷3=9.33 Therefore we can say that each gets 9 cars with 1 leftover. Question 6. An airplane flies at a speed of 474 miles per hour. How many miles does the plane fly in 5 hours? Options: a. 2,070 miles b. 2,140 miles c. 2,370 miles d. 2,730 miles Answer: c. 2,370 miles Explanation: Number of miles flew by aeroplane in one hour= 474 Number of hours the aeroplane flew= 5 hours Total number of miles flew in 5 hours= 474 x 5= 2,370 miles ### Page No. 233 Choose the best term from the box to complete the sentence. Question 1. A number that is the product of a number and a counting number is called a _____________. ___________ Answer: Multiple Explanation: 3 x 4 = 12 In which 4 is a multiple and also 4 is a counting number Question 2. Numbers that are easy to compute mentally are called _____________. ___________ Answer: Compatible numbers Explanation: Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. Question 3. When a number cannot be divided evenly, the amount left over is called the _____________. ___________ Answer: Remainder Explanation: When we divide 10 with 3 there will be 1 remaining, which is called remainder. Divide. Draw a quick picture to help. Question 4. 26 ÷ 3 _____ R _____ Answer: Quotient: 8 Remainder: 2 Explanation: Quotient: A. Use 26 counters to represent the 26 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 8 groups by placing them in the circles. C. Number of circles filled= quotient of 26 ÷ 3 = 8 Remainder: The number of counters left over is the remainder. The number of counters leftover= 2 Question 5. 19 ÷ 4 _____ R _____ Answer: Quotient: 4 Remainder: 3 Explanation: Quotient: A. Use 19 counters to represent the 19 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of circles filled= quotient of 19 ÷ 4 = 4 Remainder: The number of counters left over is the remainder. The number of counters leftover= 3 Use basic facts and place value to find the quotient. Question 8. 3,000 ÷ 6 = _____ Answer: 500 Explanation: STEP 1 Identify the basic fact. 30 ÷ 6 STEP 2 Use place value. 3,000 = 30 hundreds STEP 3 Divide. 30 hundreds ÷ 6 = 5 hundreds 3,000 ÷ 6 = 500 Use compatible numbers to estimate the quotient. Question 9. 635 ÷ 9 about _____ Answer: 70 Explanation: What number close to 635 is easy to divide by 9? 630 is close to 635. What basic fact can you use? 630 ÷ 9 Choose 630 because it is close to 635 and can easily be divided by 9. 63 ÷ 9 = 7 630 ÷ 9 = 70 635 ÷ 9 is about 70 Question 10. 412 ÷ 5 about _____ Answer: 82 Explanation: What number close to 412 is easy to divide by 5? 410 is close to 412. What basic fact can you use? 410 ÷ 5 Choose 410 because it is close to 412 and can easily be divided by 5. 410 ÷ 5 = 82 412 ÷ 5 is about 82 Question 11. 490 ÷ 8 about _____ Answer: 60 Explanation: What number close to 490 is easy to divide by 8? 480 is close to 490. What basic fact can you use? 480 ÷ 8 Choose 480 because it is close to 490 and can easily be divided by 8. 48 ÷ 8 = 6 480 ÷ 8 = 60 490 ÷ 8 is about 60 Use grid paper or base-ten blocks to model the quotient. Then record the quotient. Question 12. 63 ÷ 3 = _____ Answer: 21 Explanation: A. Outline another model to show 63 ÷ 3. How many groups of 3 can you make? B. Think of 63 as 60 + 3. Break apart the model, label, and shade to show two divisions. 63 ÷ 3 = (60 ÷ 3 ) + (3 ÷ 3 ) = 20 + 1 = 21 Question 13. 85 ÷ 5 = _____ Answer: 17 Explanation: A. Outline another model to show 85 ÷ 5. How many groups of 5 can you make? B. Think of 85 as 80 + 5. Break apart the model, label, and shade to show two divisions. 85 ÷ 5 = (80 ÷ 5 ) + (5 ÷ 5) = 16 + 1 = 17 Question 14. 168 ÷ 8 = _____ Answer:21 Explanation: A. Outline another model to show 168 ÷ 8. How many groups of 8 can you make? B. Think of 168 as 160 + 8. Break apart the model, label, and shade to show two divisions. 168 ÷ 8 = (160 ÷ 8 ) + (8 ÷ 8 ) = 20 + 1 = 21 ### Page No. 234 Question 15. Ana has 296 coins in her coin collection. She put the same number of coins in each of 7 jars. About how many coins are in each jar? about _____ coins Answer: 42 Explanation: The total number of coins Ana has= 296 coins Number of Jars= 7 Number of coins in each Jar= 296 ÷ 7 = 42 coins Question 16. Which two estimates is the quotient 345 ÷ 8 between? _____ and _____ Answer: The quotient is between 42 and 43 Explanation: What number close to 345 is easy to divide by 8? 336 is close to 1,624. What basic fact can you use? 336 ÷ 8 Choose 336 because it is close to 345 and can easily be divided by 8. 336 ÷ 8 = 42 345 ÷ 8 is about 42 What number close to 345 is easy to divide by 8? 344 is close to 345. What basic fact can you use? 344 ÷ 8 Choose 344 because it is close to 345 and can easily be divided by 8. 344 ÷ 8 = 43 345 ÷ 8 is about 43 Question 17. A total of 8,644 people went to the football game. Of those people, 5,100 sat on the home side and the rest sat on the visitor’s side. If the people sitting on the visitor’s side filled 8 equal-sized sections, how many people sat in each of the sections? about _____ people Answer: 443 Explanation: Total number of people in the football game= 8,644 Number of people who sat on the homeside= 5,100 Number of people who sat on the visitor’s side= 3,544 Number of equal-sized sections= 8 Number of people who sat in each of the sections= 3,544 ÷ 8= 443 ### Page No. 237 Use repeated subtraction to divide. Question 1. 84 ÷ 7 _____ Answer: 12 Explanation: A. Begin with 84 counters. Subtract 7 counters. B. Subtract 7 counters from 84 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 12. Question 2. 60 ÷ 4 _____ Answer: 15 Explanation: A. Begin with 60 counters. Subtract 4 counters. B. Subtract 4 counters from 60 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 15. Question 3. 91 ÷ 8 _____ R _____ Answer: 11.3=11(approx) Explanation: A. Begin with 91 counters. Subtract 8 counters. B. Subtract 8 counters from 91 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 11 Draw a number line to divide. Question 4. 65 ÷ 5 = _____ Answer: 13 Explanation: A. Begin with 65 counters. Subtract 5 counters. B. Subtract 5 counters from 65 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 13 Question 5. Use Appropriate Tools Can you divide 32 by 3 evenly? Use the number line to explain your answer. Type below: __________ Answer: 11 (approx) Explanation: How many equal groups of 3 did you subtract? So, 32 ÷ 3 = 10.8=11(approx). ### Page No. 238 Question 7. A new playground will be 108 feet long. Builders need to allow 9 feet of space for each piece of climbing equipment. They want to put as many climbers along the length of the playground as possible. How many climbers can they place? a. What are you asked to find? Type below: __________ Answer: 12 Explanation: A. Begin with 108 counters. Subtract 9 counters. B. Subtract 9 counters from 108 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 12. Question 7. b. How can you use repeated subtraction to solve the problem? Type below: __________ Answer: Repeated subtraction is a method to solve and find the quotient. Explanation: Example: A. Begin with 65 counters. Subtract 5 counters. B. Subtract 5 counters from 65 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 13 Question 7. c. Tell why you might use multiples of the divisor to solve the problem. Type below: __________ Answer: The multiple which divides 108 is 12 Explanation: The number 108 has multiples which divide 108 evenly, 1 x 108 =108 2 x 54 =108 3 x 36 =108 4 x 27 =108 6 x 18 =108 9 x 12 =108 12 x 9 =108 18 x 6 =108 27 x 4 =108 36 x 3 =108 54 x 2 =108 108 x 1 =108 Multiples which divide 108 are 1,2,3,4,5,6,9,12,18,27,36,54,108. Question 7. d. Show steps to solve the problem. Type below: __________ Answer: 108 ÷ 9 =12 Explanation: A. Begin with 108 counters. Subtract 9 counters. B. Subtract 9 counters from 108 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 12 Question 7. e. Complete the sentences. There are _______ equal parts of the playground, each _______ feet long. So, _______ climbers can fit along the length of the playground. Type below: __________ Answer: There are ___108____ equal parts of the playground, each __09_____ feet long. So, __12_____ climbers can fit along the length of the playground. Explanation: A new playground will be 108 feet long. Builders need to allow 9 feet of space for each piece of climbing equipment. Number of climbers that can fit along the length of the playground= 108 ÷ 9 =12 Question 8. Which model matches each expression? Write the letter on the line next to the model. Type below: __________ Answer: 240 ÷ 80 expression resembles the second model while 240 ÷ 60 expression resembles the first model. Explanation: 240 ÷ 80 A. Draw a number line with 80 as each interval. B. Draw up to 240 and count the intervals, it gives the quotient. C. The quotient is 3 240 ÷ 60 A. Draw a number line with 60 as each interval. B. Draw up to 240 and count the intervals, it gives the quotient. C. The quotient is 4 ### Common Core – Page No. 239 Divide Using Repeated Subtraction Use repeated subtraction to divide. Question 1. 42 ÷ 3 = 14 3)$$\overline { 42 }$$ -30 ← 10 × 3 | 10 ——- 12 -12 ← 4 × 3 | +4 ——- ———– 0 14 Answer: 14 Explanation: A. Begin with 42 counters. Subtract 3 counters. B. Subtract 3 counters from 42 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 14 Question 2. 72 ÷ 4 = _____ Answer: 18 Explanation: A. Begin with 72 counters. Subtract 4 counters. B. Subtract 4 counters from 72 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 18 Question 3. 93 ÷ 3 = _____ Answer: 31 Explanation: A. Begin with 93 counters. Subtract 3 counters. B. Subtract 3 counters from 93 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 31 Question 4. 35 ÷ 4 = _____ r _____ Answer: 8r3 Explanation: Quotient: A. Use 35 counters to represent the 35 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 35 ÷ 4 D. Number of circles are equally filled with 4 counters, therefore, the quotient is 8 Remainder: The number of counters left over is the remainder. The number of counters leftover= 3 For 35 ÷ 4, the quotient is 8 and the remainder is 3, or 8 r3. Question 5. 93 ÷ 10 = _____ r _____ Answer: 9r3 Explanation: Quotient: A. Use 93 counters to represent the 93 dominoes. Then draw 10 circles to represent the divisor. B. Share the counters equally among the 10 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 93 ÷ 10 D. Number of circles are equally filled with 10 counters, therefore, the quotient is 9 Remainder: The number of counters left over is the remainder. The number of counters leftover= 3 For 93 ÷ 10, the quotient is 9 and the remainder is 3, or 9 r3. Question 6. 86 ÷ 9 = _____ r _____ Answer: 9r5 Explanation: Quotient: A. Use 86 counters to represent the 86 dominoes. Then draw 9 circles to represent the divisor. B. Share the counters equally among the 9 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 86 ÷ 9 D. Number of circles are equally filled with 9 counters, therefore, the quotient is 9 Remainder: The number of counters left over is the remainder. The number of counters leftover= 5 For 86 ÷ 9, the quotient is 9 and the remainder is 5, or 9 r5. Draw a number line to divide. Question 7. 70 ÷ 5 = _____ Answer: 14 Explanation: A. Draw a number line with 5 as each interval. B. Draw up to 70 and count the intervals, it gives the quotient. C. The quotient is 14 Problem Solving ### Common Core – Page No. 240 Lesson Check Question 1. Randall collects postcards that his friends send him when they travel. He can put 6 cards on one scrapbook page. How many pages does Randall need to fit 42 postcards? Options: a. 3 b. 4 c. 6 d. 7 Answer: d. 7 Explanation: Total number of postcards Randall has = 42 postcards Number of postcards on one scrapbook page = 6 cards Number of pages needed to fit the postcards = 42 ÷ 6=7 Question 2. Ari stocks shelves at a grocery store. He puts 35 cans of juice on each shelf. The shelf has 4 equal rows and another row with only 3 cans. How many cans are in each of the equal rows? Options: a. 6 b. 7 c. 8 d. 9 Answer: c. 8 Explanation: Total number of cans of juice on each shelf = 35 Number of rows = 4 Number of cans on the other shelf = 3 Number of cans placed on the first shelf = 35 – 3 = 32 Number of juice cans in the first row = 32 ÷ 4 = 8 cans Spiral Review Question 3. Fiona sorted her CDs into separate bins. She placed 4 CDs in each bin. If she has 160 CDs, how many bins did she fill? Options: a. 4 b. 16 c. 40 d. 156 Answer: c. 40 Explanation: Total number of CD’s in Fiona has = 160 CD’s Number of CD’s placed in each bin = 4 Number of bins required to place the CD’s = 160 ÷ 4 = 40 Question 4. Eamon is arranging 39 books on 3 shelves. If he puts the same number of books on each shelf, how many books will there be on each shelf? Options: a. 11 b. 12 c. 13 d. 14 Answer: c. 13 Explanation: Total number of books Eamon has = 39 books Number of shelves = 3 Number of books in each shelf = 39 ÷ 3 = 13 Question 5. A newborn boa constrictor measures 18 inches long. An adult boa constrictor measures 9 times the length of the newborn plus 2 inches. How long is the adult? Options: a. 142 inches b. 162 inches c. 164 inches d. 172 inches Answer: c. 164 inches Explanation: Length of newborn boa constrictor = 18 inches Length of an adult boa constrictor = 9 x Length of newborn boa constrictor = 9 x 18 = 162 Total length of an adult boa constrictor = 162 + 2 = 164 inches Question 6. Madison has 6 rolls of coins. Each roll has 20 coins. How many coins does Madison have in all? Options: a. 110 b. 120 c. 125 d. 130 Answer: b. 120 Explanation: Number of rolls of coins = 6 Number of coins in each roll = 20 Total number of coins Madison has = 20 x 6 = 120 ### Page No. 243 Question 1. Lacrosse is played on a field 330 ft long. How many yards long is a lacrosse field? (3 feet = 1 yard) Divide. Use partial quotients. So, the lacrosse field is _____ yards long. ______ yards Answer: 37 yards (approx) Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. For example, you know that you can make at least 100 ft which is long 33 yards. Continue subtracting until the remaining number is less than the multiple, 3. STEP 2 Subtract smaller multiples, such as 3 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 110 ft = 110 ÷ 3 = 36.6 yards = 37 yards (approx). Divide. Use partial quotients. Question 2. 3)$$\overline { 225 }$$ ____ Answer: 75 Explanation: STEP 1 Start by subtracting a greater multiple, such as 50 times the divisor. Continue subtracting until the remaining number is less than the multiple, 3. STEP 2 Subtract smaller multiples, such as 3 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 50 x 3 = 150 : 225 – 150 = 75 3 x 25 = 75 : 75 – 75 = 0 Therefore the quotient is 75 ( 50 + 25) Divide. Use rectangular models to record the partial quotients. Question 3. 428 ÷ 4 = ____ Answer: 107 Explanation: STEP 1 Start by subtracting a greater multiple, such as 50 times the divisor. Continue subtracting until the remaining number is less than the multiple, 4. STEP 2 Subtract smaller multiples, such as 4 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 50 x 4 = 200 : 428 – 200 = 228 4 x 50 = 200 : 228 – 200 = 28 7 x 4 = 28 : 28 – 28 = 0 Therefore the quotient is 107 ( 50 + 50 + 7) The rectangle models are given below : Divide. Use partial quotients. Question 4. 7)$$\overline { 224 }$$ ____ Answer: 32 Explanation: STEP 1 Start by subtracting a greater multiple, such as 30 times the divisor. Continue subtracting until the remaining number is less than the multiple, 7. STEP 2 Subtract smaller multiples, such as 7 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 30 x 7 = 210 : 224 – 210 = 14 7 x 2 = 14 : 14 – 14 = 0 Therefore the quotient is 32 ( 30 + 2) Question 5. 7)$$\overline { 259 }$$ ____ Answer: 37 Explanation: STEP 1 Start by subtracting a greater multiple, such as 30 times the divisor. Continue subtracting until the remaining number is less than the multiple, 7. STEP 2 Subtract smaller multiples, such as 7 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 30 x 7 = 210 : 225 – 210 = 49 7 x 7 = 49 : 49 – 49 = 0 Therefore the quotient is 37 ( 30 + 7) Question 6. 8)$$\overline { 864 }$$ ____ Answer: 108 Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 8. STEP 2 Subtract smaller multiples, such as 8 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 8 = 800 : 864 – 800 = 64 8 x 8 = 64 : 64 – 64 = 0 Therefore the quotient is 108 ( 100 + 8) Question 7. 6)$$\overline { 738 }$$ ____ Answer: 123 Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 6. STEP 2 Subtract smaller multiples, such as 6 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 6 = 600 : 738 – 600 = 138 6 x 23 = 138 : 138 – 138 = 0 Therefore the quotient is 123 ( 100 + 23) Divide. Use rectangular models to record the partial quotients. Question 8. 328 ÷ 2 = ____ Answer: 164 Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 2. STEP 2 Subtract smaller multiples, such as 2 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 2 = 200 : 328 – 200 = 128 2 x 64 = 128 : 128 – 128 = 0 Therefore the quotient is 164 ( 100 + 64) The rectangle models are given below : Question 9. 475 ÷ 5 = ____ Answer: 95 Explanation: STEP 1 Start by subtracting a greater multiple, such as 90 times the divisor. Continue subtracting until the remaining number is less than the multiple, 5. STEP 2 Subtract smaller multiples, such as 5 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 90 x 5 = 450 : 475 – 450 = 25 5 x 5 = 25 : 25 – 25 = 0 Therefore the quotient is 95 (90 + 5) The rectangle models are given below : Question 10. 219 ÷ 3 = ____ Answer: 73 Explanation: STEP 1 Start by subtracting a greater multiple, such as 70 times the divisor. Continue subtracting until the remaining number is less than the multiple, 3. STEP 2 Subtract smaller multiples, such as 3 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 70 x 3 = 210 : 219 – 210 = 9 3 x 3 = 9 : 9 – 9 = 0 Therefore the quotient is 73 ( 70 + 3) The rectangle models are given below : Question 11. 488 ÷ 4 = ____ Answer: 122 Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 4. STEP 2 Subtract smaller multiples, such as 4 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 4 = 400 : 488 – 400 = 88 4 x 22 = 88 : 88 – 88 = 0 Therefore the quotient is 122 ( 100 + 22) The rectangle models are given below : Question 12. Use Reasoning What is the least number you can divide by 5 to get a three-digit quotient? Explain how you found your answer. ____ Answer: The quotient can be a three-digit number or a two-digit number. Explanation: Example: 475 ÷ 5 = ____ Answer: 95 Explanation: STEP 1 Start by subtracting a greater multiple, such as 90 times the divisor. Continue subtracting until the remaining number is less than the multiple, 5. STEP 2 Subtract smaller multiples, such as 5 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 90 x 5 = 450 : 475 – 450 = 25 5 x 5 = 25 : 25 – 25 = 0 Therefore the quotient is 95 (90 + 5) ### Page No. 244 Use the table for 13–15. Question 13. Rob wants to put 8 baseball cards on each page in an album. How many pages will he fill? ____ pages Answer: 31 pages Explanation: Total number of baseball cards = 248 Number of cards in each page = 8 Number of pages required = 248 ÷ 8 = 31 pages Question 14. Rob filled 5 plastic boxes with hockey cards. There were the same number of cards in each box. How many cards did he put in each box? How many cards were left over? Type below: ___________ Answer: There where 12 hockey cards in each box, number of cards leftover = 4 Explanation: Total number of hockey cards = 64 Number of boxes = 5 Number of cards in each box = 64 ÷ 5 = 12.8 that is exactly 60 cards can be fit in 5 boxes and 12 in each box Number of cards leftover = 64 – 60 = 4 Question 15. Rob filled 3 fewer plastic boxes with football cards than basketball cards. He filled 9 boxes with basketball cards. How many boxes did he fill with football cards? How many football cards were in each box? ____ boxes ____ cards Answer: 6 boxes and 16 cards in each box Explanation: Number of basketball cards= 189 Number of boxes in which the basketball cards were kept= 9 boxes Number of football cards= 96 Number of boxes in which the football cards were kept = number of boxes in which the basketball cards were kept – 3 = 9-3=6boxes Number of football cards in each box = 96 ÷ 6 =16 cards Question 17. Use partial quotients. Fill in the blanks. Type below: ___________ Answer: 97 Explanation: STEP 1 Start by subtracting a greater multiple, such as 80 times the divisor. Continue subtracting until the remaining number is less than the multiple, 5. STEP 2 Subtract smaller multiples, such as 5 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 80 x 5 = 400 : 485 – 400 = 85 5 x 17 = 85 : 85 – 85 = 0 Therefore the quotient is 97 ( 80 + 17) ### Common Core – Page No. 245 Divide Using Partial Quotients Divide. Use partial quotients. Question 1. 8)$$\overline { 184 }$$ -80 ← 10 × 8 10 ——- 104 -80 ← 10 × 8 + 10 ——- -24 -24 ← 3 × 8 + 3 ——– ——– 0 23 Answer: 23 Explanation: STEP 1 Start by subtracting a greater multiple, such as 10 times the divisor. Continue subtracting until the remaining number is less than the multiple, 8. STEP 2 Subtract smaller multiples, such as 10 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 10 x 8 = 80 : 184 – 80 = 104 10 x 8 = 80 : 104 – 80 = 24 : 3 x 8 = 24 : 24 – 24 = 0 Therefore the quotient is 23 ( 10 + 10 + 3) Question 2. 6)$$\overline { 258 }$$ _____ Answer: 43 Explanation: STEP 1 Start by subtracting a greater multiple, such as 40 times the divisor. Continue subtracting until the remaining number is less than the multiple, 6. STEP 2 Subtract smaller multiples, such as 3 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 40 x 6 = 240 : 258 – 240 = 18 3 x 6 = 18 : 18 – 18 = 0 Therefore the quotient is 43 ( 40 + 3) Question 3. 5)$$\overline { 630 }$$ _____ Answer: 126 Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 5. STEP 2 Subtract smaller multiples, such as 20 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 5 = 500 : 630 – 500 = 130 5 x 20 = 100 : 130 – 100 = 30 : 5 x 6 = 30 : 30 – 30 = 0 Therefore the quotient is 126 ( 100 + 20 + 6) Divide. Use rectangular models to record the partial quotients. Question 4. 246 ÷ 3 = _____ Answer: 82 Explanation: STEP 1 Start by subtracting a greater multiple, such as 80 times the divisor. Continue subtracting until the remaining number is less than the multiple, 3. STEP 2 Subtract smaller multiples, such as 80 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 80 x 3 = 240 : 246 – 240 = 6 3 x 2 = 6 : 6 – 6 = 0 Therefore the quotient is 82 ( 80 + 2) The rectangle models are given below : Question 5. 126 ÷ 2 = _____ Answer: 63 Explanation: STEP 1 Start by subtracting a greater multiple, such as 60 times the divisor. Continue subtracting until the remaining number is less than the multiple,2. STEP 2 Subtract smaller multiples, such as 60 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 60 x 2 = 120 : 126 – 120 = 6 2 x 3 = 6 : 6 – 6 = 0 Therefore the quotient is 63 ( 60 +3) The rectangle models are given below : Question 6. 605 ÷ 5 = _____ Answer: 121 Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 5. STEP 2 Subtract smaller multiples, such as 20 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 5 = 500 : 605 – 500 = 105 5 x 20 = 100 : 105 – 100 = 5 : 5 x 1 = 5 : 5 – 5 = 0 Therefore the quotient is 121 ( 100 + 20 + 1) The rectangle models are given below : Divide. Use either way to record the partial quotients. Question 7. 492 ÷ 3 = _____ Answer: 164 Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 3. STEP 2 Subtract smaller multiples, such as 50 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 3 = 300 : 492 – 300 = 192 50 x 3 = 150 : 192 – 150 = 42 : 3 x 14 = 42 : 42 – 42 = 0 Therefore the quotient is 164 ( 100 + 50 + 14) Question 8. 224 ÷ 7 = _____ Answer: 32 Explanation: STEP 1 Start by subtracting a greater multiple, such as 30 times the divisor. Continue subtracting until the remaining number is less than the multiple, 7. STEP 2 Subtract smaller multiples, such as 30 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 30 x 7 = 210 : 224 – 210 = 14 7 x 2 = 14 : 14 – 14 = 0 Therefore the quotient is 32 ( 30 + 2) Question 9. 692 ÷ 4 = _____ Answer: 173 Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 4. STEP 2 Subtract smaller multiples, such as 100 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 4 = 400 : 692 – 400 = 392 4 x 50 = 200 : 392 – 200 = 192 : 4 x 48 = 192 : 192 – 192 = 0 Therefore the quotient is 198 ( 100 + 50 + 48) Problem Solving Question 10. Allison took 112 photos on vacation. She wants to put them in a photo album that holds 4 photos on each page. How many pages can she fill? _____ pages Answer: 28 Explanation: STEP 1 Start by subtracting a greater multiple, such as 20 times the divisor. Continue subtracting until the remaining number is less than the multiple, 4. STEP 2 Subtract smaller multiples, such as 20 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 20 x 4 = 80 : 112 – 80 = 32 4 x 8 = 32 : 32 – 32 = 0 Therefore the quotient is 28 ( 20 + 8) Question 11. Hector saved$726 in 6 months. He saved the same amount each month. How much did Hector save each month?
$_____ Answer:$121

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 6.
STEP 2
Subtract smaller multiples, such as 100 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 6 = 600 : 726 – 600 = 126
6 x 20 = 120 : 126 – 120 = 6 : 6 x 1 = 6 : 6 – 6 = 0
Therefore the quotient is 121 ( 100 + 20 +1)

### Common Core – Page No. 246

Lesson Check

Question 1.
Annaka used partial quotients to divide 145 ÷ 5. Which shows a possible sum of partial quotients?
Options:
a. 50 + 50 + 45
b. 100 + 40 + 5
c. 10 + 10 + 9
d. 10 + 4 + 5

Answer: c. 10 + 10 + 9

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 4.
STEP 2
Subtract smaller multiples, such as 10 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 10 x 5 = 50 : 145 – 50 = 95
5 x 10 = 50 : 95 – 50 = 45 : 5 x 9 = 45 : 45 – 45 = 0
Therefore the quotient is 29 ( 10 + 10 +9)

Question 2.
Mel used partial quotients to find the quotient 378 ÷ 3. Which might show the partial quotients that Mel found?
Options:
a. 100, 10, 10, 9
b. 100, 10, 10, 6
c. 100, 30, 30, 6
d. 300, 70, 8

Answer: b. 100, 10, 10, 6

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 3.
STEP 2
Subtract smaller multiples, such as 10 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 3 = 300 : 378 – 300 = 78
10 x 3 =30 : 78 – 30 = 48 : 3 x 16 = 48 : 48 – 48 = 0
Therefore the quotient is 126 ( 100 + 10 +10 + 6)

Spiral Review

Question 3.
What are the partial products of 42 × 5?
Options:
a. 9 and 7
b. 20 and 10
c. 200 and 7
d. 200 and 10

Explanation:
STEP1
42 x 5
Start by multiplying the digit five with the units digit 2 = 5 x 2 =10
Multiply the digit 5 with 4 in the tens place = 4 x 5 = 20
Since 4 is in the tens place when we multiply 4 and 5 we must place it in the hundreds place by assuming units digit to be zero.
Therefore, the partial product of 42 x 5 = 200

Question 4.
Mr. Watson buys 4 gallons of paint that cost $34 per gallon. How much does Mr. Watson spend on paint? Options: a.$38
b. $126 c.$136
d. $1,216 Answer: c.$136

Explanation:
Cost of each gallon of paint = $34 Number of gallons = 4 The total cost of the gallons =$ 34 x 4 = $136 Question 5. Use the area model to find the product 28 × 32. Options: a. 840 b. 856 c. 880 d. 896 Answer: d. 896 Explanation: The whole rectangle is divided into four small rectangles the areas of these rectangles are: Area of yellow rectangle= 30 x 20=600 Area of green rectangle= 2 x 20 = 40 Area of pink rectangle= 8 x 30= 240 Area of blue rectangle= 2 x 8= 16 Product of 32 and 28 = Area of yellow rectangle + Area of green rectangle + Area of pink rectangle + Area of the blue rectangle = 600+40+240+16 = 896 Question 6. An adult male lion eats about 108 pounds of meat per week. About how much meat does an adult male lion eat in one day? Options: a. about 14 pounds b. about 15 pounds c. about 16 pounds d. about 17 pounds Answer: b. about 15 pounds Explanation: Mass of meat an adult lion eats in one week = 108 Number of days in a week = 7 Mass of meat ate by the lion in one day = 108 ÷ 7 = 15.4 pounds = about 15 pounds ### Page No. 249 Divide. Use base-ten blocks. Question 1. 48 ÷ 3 _____ Answer: 16 Explanation: A. Draw 3 circles to represent the divisor. Then use base-ten blocks to model 48. Show 48 as 4 tens and 8 ones. B. Share the tens equally among the 3 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 3 groups. D. There are 1 ten(s) and 6 one(s) in each group. So, the quotient is 16. Question 4. Divide. Draw a quick picture. Record the steps. 84 ÷ 3 _____ Answer: 28 Explanation: STEPS: A. Draw 3 circles to represent the divisor. Then use base-ten blocks to model 84. Show 84 as 8 tens and 4 ones. B. Share the tens equally among the 3 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 3 groups. D. There are 2 ten(s) and 8 one(s) in each group. So, the quotient is 28. Question 5. Explain why you did not need to regroup in Exercise 2. Type below: ___________ Answer: We did not regroup in exercise two because we used the method of counters in which we placed the counters one after the other in the circles and concluded with number of counters in each group and the number of counters left over. Explanation: Example: 28 ÷ 3(in the form of exercise 2) A. Use 28 counters to represent the 28 dominoes. Then draw 3 circles to represent the 3 players. B. Share the counters equally among the 3 groups by placing them in the circles. C. Find the number of counters in each group and the number of counters left over. Record your answer. 9 counters in each group and 3 counters are leftover. Example: 84 ÷ 3 A. Draw 3 circles to represent the divisor. Then use base-ten blocks to model 84. Show 84 as 8 tens and 4 ones. B. Share the tens equally among the 3 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 3 groups. D. There are 2 ten(s) and 8 one(s) in each group. So, the quotient is 28. Question 6. Mindy is preparing fruit boxes for gifts. She divides 36 apples evenly into 6 boxes. Then she divided 54 bananas evenly into the same 6 boxes. How many pieces of fruit are in each of Mindy’s boxes? _____ pieces of fruit Answer: 6+9=15 pieces of fruits are in each box of Mindy’s Explanation: Total number of apples = 36 Number of boxes in which the apples were kept = 6 Number of apple pieces in each box = 36 ÷ 6 = 6 Total number of bananas = 54 Number of boxes in which the bananas were kept = 6 Number of banana pieces in each box = 54 ÷ 6 = 9 Total number of fruit pieces in each box = 9 + 6 = 15 Question 7. Ami needs to divide these base-ten blocks into 4 equal groups. Describe a model that would show how many are in each group. Type below: ___________ Answer: 14 Explanation: A. Draw 4 circles to represent the divisor. Then use base-ten blocks to model 56. Show 56 as 5 tens and 6 ones. B. Share the tens equally among the 4 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 4 groups. D. There are 1 ten(s) and 4 one(s) in each group. So, the quotient is 14. ### Page No. 250 Sense or Nonsense? Question 8. Angela and Zach drew quick pictures to find 68 ÷ 4. Whose quick picture makes sense? Whose quick picture is nonsense? Explain your reasoning. Type below: ___________ Answer: Zach’s quick picture is correct while Angela’s is not correct. Explanation: A. Draw 4 circles to represent the divisor. Then use base-ten blocks to model 68. Show 68 as 6 tens and 8 ones. B. Share the tens equally among the 4 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 4 groups. D. There are 1 ten(s) and 7 one(s) in each group. So, the quotient is 17. Hence Zach’s statement and the quick picture are correct. Question 9. Analyze What did Angela forget to do after she shared the tens equally among the 4 groups? Type below: ___________ Answer: Angela forgot to regroup the leftover tens into ones. Share the ones equally among the 4 groups. Explanation: Since there are 6 tens and 4 circles only 4 tens can be placed in them while the other 2 tens are leftover which must be converted into 20 ones. ### Common Core – Page No. 251 Model Division with Regrouping Divide. Use base-ten blocks. Question 1. 63 ÷ 4 = 15 r3 Answer: 15 r 3 Explanation: A. Draw 4 circles to represent the divisor. Then use base-ten blocks to model 63. Show 63 as 6 tens and 3 ones. B. Share the tens equally among the 4 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 4 groups. D. There are 1 ten(s) and 5 one(s) in each group. So, the quotient is 15. E. After grouping, there are 3 blocks which weren’t grouped. So, the remainder is 3 Question 2. 83 ÷ 3 _____ R _____ Answer: 27 r 2 Explanation: A. Draw 3 circles to represent the divisor. Then use base-ten blocks to model 83. Show 83 as 8 tens and 3 ones. B. Share the tens equally among the 3 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 3 groups. D. There are 2 ten(s) and 7 one(s) in each group. So, the quotient is 27. E. After grouping, there are 2 blocks which weren’t grouped. So, the remainder is 2 Divide. Draw quick pictures. Record the steps. Question 3. 85 ÷ 5 _____ Answer: 17 Explanation: A. Draw 5 circles to represent the divisor. Then use base-ten blocks to model 85. Show 85 as 8 tens and 5 ones. B. Share the tens equally among the 5 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 5 groups. D. There are 1 ten(s) and 7 one(s) in each group. So, the quotient is 17. Question 4. 97 ÷ 4 _____ R _____ Answer: 24 r 1 Explanation: A. Draw 4 circles to represent the divisor. Then use base-ten blocks to model 97. Show 97 as 9 tens and 7 ones. B. Share the tens equally among the 4 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 4 groups. D. There are 2 ten(s) and 4 one(s) in each group. So, the quotient is 24. E. After grouping, there is 1 block which wasn’t grouped. So, the remainder is 1 Problem Solving ### Common Core – Page No. 252 Lesson Check Question 1. Gail bought 80 buttons to put on the shirts she makes. She uses 5 buttons for each shirt. How many shirts can Gail make with the buttons she bought? Options: a. 14 b. 16 c. 17 d. 18 Answer: b. 16 Explanation: Total number of buttons = 80 Number of buttons used for each shirt = 5 Number of shirts she can make = 80 ÷ 5 =16 Question 2. Marty counted how many breaths he took in 3 minutes. In that time, he took 51 breaths. He took the same number of breaths each minute. How many breaths did Marty take in one minute? Options: a. 15 b. 16 c. 17 d. 19 Answer: c. 17 Explanation: Total number of breaths Marty counted = 51 Time in which the breath was counted = 3 minutes Number of breaths in one minute = 51 ÷ 3 = 17 Spiral Review Question 3. Kate is solving brain teasers. She solved 6 brain teasers in 72 minutes. How long did she spend on each brain teaser? Options: a. 12 minutes b. 14 minutes c. 18 minutes d. 22 minutes Answer: a. 12 minutes Explanation: Number of brain teasers solved = 6 Number of minutes spent on brain teasers = 72 minutes Number of minutes spent on each problem = 72 ÷ 6 =12 minutes Question 4. Jenny works at a package delivery store. She puts mailing stickers on packages. Each package needs 5 stickers. How many stickers will Jenny use if she is mailing 105 packages? Options: a. 725 b. 625 c. 525 d. 21 Answer: c. 525 Explanation: Number of packages = 105 Number of stickers on each package = 5 Total number of stickers on the packages = 105 x 5 = 525 Question 5. The Puzzle Company packs standardsized puzzles into boxes that hold 8 puzzles. How many boxes would it take to pack up 192 standard-sized puzzles? Options: a. 12 b. 16 c. 22 d. 24 Answer: d. 24 Explanation: Total number of puzzles = 192 Number of puzzles in each box = 8 Number of boxes used = 192 ÷ 8 = 24 boxes Question 6. Mt. Whitney in California is 14,494 feet tall. Mt. McKinley in Alaska is 5,826 feet taller than Mt. Whitney. How tall is Mt. McKinley? Options: a. 21,310 feet b. 20,320 feet c. 20,230 feet d. 19,310 feet Answer: b. 20,320 feet Explanation: Height of Mt. Whitney in California = 14,494 feet Height of Mt. McKinley in Alaska is 5,826 feet taller than Mt. Whitney. Therefore the height of Mt. McKinley in Alaska = 14,494 feet + 5,826 feet = 20,320 feet ### Page No. 255 Question 1. There are 452 pictures of dogs in 4 equal groups. How many pictures are in each group? Explain how you can use place value to place the first digit in the quotient. ______ pictures Answer: 113 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 452. 400 hundred can be shared among 4 groups without regrouping. Now there is 1 ten to share among 4 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 45 ÷ 4 Multiply. 4 × 11 = 44 Subtract. 45 − 44 = 1 tens STEP 3 Divide the ones. Regroup 1 ten as 10 ones. Now there are 12 ones to share among 4 groups. Divide. 12 ones ÷ 4 Multiply. 4×3 ones Subtract. 12 ones − 12 ones = 0 So, the quotient is 113 Divide. Question 2. 4)$$\overline { 166 }$$ ______ R ______ Answer: 41 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 166. 1 hundred cannot be shared among 4 groups without regrouping. Now there is 1 ten to share among 4 groups. The first digit of the quotient will be in the tens place. STEP 2 Divide the tens. Divide. 166 ÷ 4 Multiply. 4 × 40 = 160 Subtract. 166 − 160 = 6 STEP 3 Divide the ones. Now there are 6 ones to share among 4 groups. Divide. 6 ones ÷ 4 Multiply. 4×1 ones Subtract. 6 ones − 4 ones = 2 So, the quotient is 41 and remainder is 2 Question 3. 5)$$\overline { 775 }$$ ______ Answer: 155 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 775. 700 hundred can be shared among 5 groups without regrouping. Now there is 70 ten to share among 5 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 700 ÷ 5 Multiply. 5 × 140 = 700 Subtract. 700 − 700 = 0 STEP 3 Divide the ones. Now there are 70 tens to share among 5 groups. Divide. 70 tens ÷ 5 Multiply. 5×14 Subtract. 75 − 70 tens = 5 ones Multiply 5 x 1 = 5 Subtract 5 ÷ 5 = 0 So, the quotient is 155 (140 + 14 + 1) Question 4. 4)$$\overline { 284 }$$ ______ Answer: 71 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 284. 200 hundred can be shared among 4 groups without regrouping. Now there are 20 tens to share among 4 groups. The first digit of the quotient will be in the tens place. STEP 2 Divide the tens. Divide. 200 ÷ 4 Multiply. 4 × 50 = 200 Subtract. 20 − 20 = 0 tens STEP 3 Divide the ones. Now there are 80 tens to share among 4 groups. Divide. 80 tens ÷ 4 Multiply. 4×20 = 80 Subtract. 80 tens − 80 tens = 0 ones There are 4 ones Multiply 4 x 1 = 4 Subtract 4-4 =0 So, the quotient is 71 (50+20+1) Question 5. 5)$$\overline { 394 }$$ ______ R ______ Answer: 78 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 394. 300 hundred can be shared among 5 groups without regrouping. Now there is 30 ten to share among 5 groups. The first digit of the quotient will be in the tens place. STEP 2 Divide the tens. Divide. 300 ÷ 5 Multiply. 5 × 60 = 300 Subtract. 300 − 300 = 0 tens STEP 3 Divide the tens. Now there are 9 tens to share among 5 groups. Divide. 9 tens ÷ 5 Multiply. 5×18 tens Subtract. 90 tens − 90 tens = 0 ones There are 4 ones 4 is the remainder. So, the quotient is 78(60+18) Question 6. 3)$$\overline { 465 }$$ ______ Answer: 155 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 465. 400 hundred can be shared among 3 groups without regrouping. Now there are 40 tens to share among 3 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 400 ÷ 3 Multiply. 3 × 130 = 390 Subtract. 400 − 390 = 1 tens STEP 3 Divide the tens. Now there are 7 tens and 5 ones to share among 3 groups. Divide. 75 ÷ 3 Multiply. 3 × 25 = 75 Subtract. 75 tens − 75 tens = 0 So, the quotient is 155 ( 130+ 25) Question 7. 8)$$\overline { 272 }$$ ______ Answer: 34 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 272. 200 hundred can be shared among 8 groups without regrouping. Now there is 27 tens and 2 ones to share among 8 groups. The first digit of the quotient will be in the tens place. STEP 2 Divide the tens. Divide. 270 ÷ 8 Multiply. 8 × 30 = 240 Subtract. 270 − 240 = 3 tens STEP 3 Divide the ones. Regroup 3 tens as 30 ones. Now there are 30 + 2 = 32 ones to share among 8 groups. Divide. 32 ones ÷ 8 Multiply. 8×4 ones Subtract. 32 ones − 32 ones = 0 So, the quotient is 34 (30 + 4) Practice: Copy and Solve Divide. Question 8. 516 ÷ 2 = ______ Answer: 258 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 516. 500 hundred can be shared among 2 groups without regrouping. Now there is 50 tens and 16 ones to share among 2 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 500 ÷ 2 Multiply. 2 × 250 = 500 Subtract. 516 − 500 = 16 ones STEP 3 Divide the ones. Now there are 16 ones to share among 2 groups. Divide. 16 ones ÷ 2 Multiply. 2×8 ones Subtract. 16 ones − 16 ones = 0 So, the quotient is 258 (250 + 8) Question 9. 516 ÷ 3 = ______ Answer: 172 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 516. 500 hundred can be shared among 3 groups without regrouping. Now there is 50 tens and 16 ones to share among 3 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 500 ÷ 3 Multiply. 3 × 160 = 480 Subtract. 516 − 480 = 36 ones STEP 3 Divide the ones. Now there are 36 ones to share among 3 groups. Divide. 36 ones ÷ 3 Multiply. 3×12 ones Subtract. 36 ones − 36 ones = 0 So, the quotient is 172 (160 + 12) Question 10. 516 ÷ 4 = ______ Answer: 129 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 516. 500 hundred can be shared among 4 groups without regrouping. Now there is 50 tens and 16 ones to share among 4 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 500 ÷ 4 Multiply. 4 × 125 = 500 Subtract. 516 − 500 = 16 ones STEP 3 Divide the ones. Now there are 16 ones to share among 4 groups. Divide. 16 ones ÷ 4 Multiply. 4×4 ones Subtract. 16 ones − 16 ones = 0 So, the quotient is 129 (125 + 4) Question 11. 516 ÷ 5 = ______ R ______ Answer: 103 R 1 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 516. 500 hundred can be shared among 5 groups without regrouping. Now there is 50 tens and 16 ones to share among 5 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 500 ÷ 5 Multiply. 5 × 100 = 500 Subtract. 516 − 500 = 16 ones STEP 3 Divide the ones. Now there are 16 ones to share among 5 groups. Divide. 16 ones ÷ 5 Multiply. 5×3 ones Subtract. 16 ones − 15 ones = 1 one So, the quotient is 103 (100 + 3) and the remainder is 1 Question 12. Look back at your answers to Exercises 8–11. What happens to the quotient when the divisor increases? Explain. The quotient ______ Answer: The quotient gets decreased when we increase the divisor. Explanation: Example: 516 ÷ 4 = ______ Answer: 129 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 516. 500 hundred can be shared among 4 groups without regrouping. Now there is 50 tens and 16 ones to share among 4 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 500 ÷ 4 Multiply. 4 × 125 = 500 Subtract. 516 − 500 = 16 ones STEP 3 Divide the ones. Now there are 16 ones to share among 4 groups. Divide. 16 ones ÷ 4 Multiply. 4×4 ones Subtract. 16 ones − 16 ones = 0 So, the quotient is 129 (125 + 4) 516 ÷ 5 = ______ R ______ Answer: 103 R 1 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 516. 500 hundred can be shared among 5 groups without regrouping. Now there is 50 tens and 16 ones to share among 5 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 500 ÷ 5 Multiply. 5 × 100 = 500 Subtract. 516 − 500 = 16 ones STEP 3 Divide the ones. Now there are 16 ones to share among 5 groups. Divide. 16 ones ÷ 5 Multiply. 5×3 ones Subtract. 16 ones − 15 ones = 1 one So, the quotient is 103 (100 + 3) and the remainder is 1 ### Page No. 256 Question 15. Nan wants to put 234 pictures in an album with a blue cover. How many full pages will she have in her album? a. What do you need to find? Type below: _________ Answer: How many full pages will she have in her album? We can find number of pictures in blue pages? We can find number of pictures in green pages? We can find number of pictures in red pages? Explanation: Question 15. b. How will you use division to find the number of full pages? Type below: _________ Answer: Since the total number of pictures and the number of colour pages are given we can divide the total number of pictures are the number of pages to find the number of full pages. Explanation: Total number of pictures =234 Number of pictures per page = 4 + 6+ 8 = 18 Number of full pages = 234 ÷ 18 =13 Question 15. c. Show the steps you will use to solve the problem. Type below: _________ Answer: 13 Explanation: Total number of pictures =234 Number of pictures per page = 4 + 6+ 8 = 18 Number of full pages = 234 ÷ 18 =13 Question 15. d. Complete the following sentences. Nan has _______ pictures. She wants to put the pictures in an album with pages that each hold _______ pictures. She will have an album with _______ full pages and _______ pictures on another page. Type below: _________ Answer: 234 pictures, 18 pictures, 13 full pages, 0 pictures on another page Explanation: Total number of pictures =234 Number of pictures per page = 4 + 6+ 8 = 18 Number of full pages = 234 ÷ 18 =13 full pages Since the remainder is 0 the number of pictures on another page = 0 Question 16. Mr. Parsons bought 293 apples to make pies for his shop. Six apples are needed for each pie. If Mr. Parsons makes the greatest number of apple pies possible, how many apples will be left? _____ pies _____ apples left over. Answer: 48 pies and 5 apples are leftover Explanation: Total number of apples= 293 Number of apples that make a pie = 6 Number of pies = Quotient of 293 ÷ 6 = 48 Number of apples leftover = 5 Question 17. Carol needs to divide 320 stickers equally among 4 classes. In which place is the first digit of the quotient? Choose the word that completes the sentence. The first digit of the quotient is in the place. _________ Answer: tens Explanation: Total number of stickers = 320 Number of classes = 4 Number of stickers in each class = Quotient of 320 ÷ 4 = 80 The first digit of quotient is in the tens place. ### Common Core – Page No. 257 Place the First Digit Divide. Question 1. 62 ——- 3)$$\overline { 186 }$$ -18 ——- 06 -6 ——- 0 Answer: 62 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 186. 180 hundred can be shared among 3 groups without regrouping. Now there is 18 tens and 6 ones to share among 3 groups. The first digit of the quotient will be in the tens place. STEP 2 Divide the tens. Divide. 180 ÷ 3 Multiply. 3 × 60 = 180 Subtract. 186 − 180 = 6 ones STEP 3 Divide the ones. Now there are 6 ones to share among 3 groups. Divide. 6 ones ÷ 3 Multiply. 2×3 ones Subtract. 6 ones − 2 ones =0 one So, the quotient is 62 (60 + 2) and the remainder is 0 Question 2. 4)$$\overline { 298 }$$ _____ R _____ Answer: Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 298. 280 hundred can be shared among 4 groups without regrouping. Now there is 28 tens and 18 ones to share among 4 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 280 ÷ 4 Multiply. 4 × 70 = 280 Subtract. 280 − 280 = 0 ones STEP 3 Divide the ones. Now there are 18 ones to share among 4 groups. Divide. 18 ones ÷ 4 Multiply. 4×4 ones Subtract. 18 ones − 16 ones = 2 ones So, the quotient is 74 (70 + 4) and the remainder is 2 Question 3. 3)$$\overline { 461 }$$ _____ R _____ Answer: 153 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 461. 450 hundred can be shared among 3 groups without regrouping. Now there is 45 tens and 11 ones to share among 3 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 450 ÷ 3 Multiply. 3 × 150 = 450 Subtract. 450 − 450 = 0 ones STEP 3 Divide the ones. Now there are 11 ones to share among 3 groups. Divide. 11 ones ÷ 3 Multiply. 3×3 ones Subtract. 11 ones − 9 ones = 2 ones So, the quotient is 153 (150 + 3) and the remainder is 2 Question 4. 9)$$\overline { 315 }$$ _____ R _____ Answer: 35 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 315. 310 hundred can be shared among 9 groups without regrouping. Now there is 31 tens and 5 ones to share among 9 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide.310 ÷ 9 Multiply. 9 × 30 = 270 Subtract. 310 − 270 = 40 ones STEP 3 Divide the ones. Now there are 40 + 5 = 45 ones to share among 9 groups. Divide. 45 ones ÷ 9 Multiply. 5×9 ones Subtract. 45 ones − 45 ones = 0 ones So, the quotient is 35 (30 + 5) and the remainder is 0 Question 6. 4)$$\overline { 604 }$$ _____ R _____ Answer: 151 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 604. 600 hundred can be shared among 4 groups without regrouping. Now there is 60 tens and 4 ones to share among 4 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 600 ÷ 4 Multiply. 4 × 150 = 600 Subtract. 600 − 600 = 0 ones STEP 3 Divide the ones. Now there are 4 ones to share among 4 groups. Divide. 4 ones ÷ 4 Multiply. 4×1 ones Subtract. 4 ones − 4 ones = 0 ones So, the quotient is 151 (150 + 1) and the remainder is 0 Question 7. 6)$$\overline { 796 }$$ _____ R _____ Answer: 132 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 796. 790 hundred can be shared among 6 groups without regrouping. Now there is 79 tens and 6 ones to share among 6 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 790 ÷ 6 Multiply. 6 × 131 = 786 Subtract. 790 − 786 = 4 ones STEP 3 Divide the ones. Now there are 4 + 6 = 10 ones to share among 6 groups. Divide. 10 ones ÷ 6 Multiply. 6×1 ones Subtract. 10 ones − 6 ones = 4 ones So, the quotient is 132 (131 + 1) and the remainder is 4 Question 8. 5)$$\overline { 449 }$$ _____ R _____ Answer: 89 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 449. 440 hundred can be shared among 5 groups without regrouping. Now there are 44 tens and 9 ones to share among 5 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 440 ÷ 5 Multiply. 5 × 88 = 440 Subtract. 440 − 440 = 0 ones STEP 3 Divide the ones. Now there are 9 ones to share among 5 groups. Divide. 9 ones ÷ 5 Multiply. 5×1 ones Subtract. 9 ones − 5 ones = 4 ones So, the quotient is 89 (88 + 1) and the remainder is 4 Question 9. 6)$$\overline { 756 }$$ _____ R _____ Answer: 126 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 756. 750 hundred can be shared among 6 groups without regrouping. Now there is 75 tens and 6 ones to share among 6 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 750 ÷ 6 Multiply. 6 × 125 = 750 Subtract. 750 − 750 = 0 ones STEP 3 Divide the ones. Now there are 6 ones to share among 6 groups. Divide. 6 ones ÷ 6 Multiply. 6×1 ones Subtract. 6 ones − 6 ones = 0 ones So, the quotient is 126 (125 + 1) and the remainder is 0 Question 10. 7)$$\overline { 521 }$$ _____ R _____ Answer: 74 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 521. 520 hundred can be shared among 7 groups without regrouping. Now there is 52 tens and 1 one to share among 7 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 520 ÷ 7 Multiply. 7 × 74 = 518 Subtract. 520 − 518 = 2 ones STEP 3 Divide the ones. Now there are 2 + 1 = 3 ones to share among 7 groups. Divide. 3 ones ÷ 7 (not possible) So, the quotient is 74 and the remainder is 3 Question 11. 5)$$\overline { 675 }$$ _____ R _____ Answer: 135 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 675. 670 hundred can be shared among 5 groups without regrouping. Now there is 67 tens and 5 ones to share among 5 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 670 ÷ 5 Multiply. 5 × 134 = 670 Subtract. 670 − 670 = 0 ones STEP 3 Divide the ones. Now there are 5 ones to share among 5 groups. Divide. 5 ones ÷ 5 Multiply. 5×1 ones Subtract. 5 ones − 5 ones = 0 ones So, the quotient is 135 (134 + 1) and the remainder is 0 Question 12. 8)$$\overline { 933 }$$ _____ R _____ Answer: 116 Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 933. 930 hundred can be shared among 8 groups without regrouping. Now there is 93 tens and 3 ones to share among 8 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 930 ÷ 8 Multiply. 8 × 116 = 928 Subtract. 930 − 928 = 2 ones STEP 3 Divide the ones. Now there are 2 + 3 = 5 ones to share among 8 groups. Divide. 5 ones ÷ 8 (not possible) So, the quotient is 116 (100 + 3) and the remainder is 5 Problem Solving Question 13. There are 132 projects in the science fair. If 8 projects can fit in a row, how many full rows of projects can be made? How many projects are in the row that is not full? _____ full rows _____ projects in the non-full row Answer: 16 full rows and 4 projects in the non-full row Explanation: Total number of projects = 132 Number of projects placed in full row = 8 Number of rows having full projects =Quotient of 132 ÷ 8 = 16 Number of projects in the non-full row = Remainder of 132 ÷ 8 = 4 Question 14. There are 798 calories in six 10-ounce bottles of apple juice. How many calories are there in one 10-ounce bottle of apple juice? _____ R _____ calories in one 10-ounce bottles of juice Answer: 133 calories Explanation: Number of calories in 6 bottles of apple juice = 798 Number of calories in each bottle = 798 ÷6 = 133 calories ### Common Core – Page No. 258 Lesson Check Question 1. To divide 572 ÷ 4, Stanley estimated to place the first digit of the quotient. In which place is the first digit of the quotient? Options: a. ones b. tens c. hundreds d. thousands Answer: c. hundreds Explanation: The quotient of 572÷ 4 is 143 STEP 1 Use place value to place the first digit. Look at the hundreds in 572. 560 hundred can be shared among 4 groups without regrouping. Now there is 1 ten to share among 4 groups. The first digit of the quotient will be in the hundreds place. Question 2. Onetta biked 325 miles in 5 days. If she biked the same number of miles each day, how far did she bike each day? Options: a. 1,625 miles b. 320 miles c. 65 miles d. 61 miles Answer: c. 65 miles Explanation: Total number of miles biked = 325 miles Number of days biked = 5 Number of miles biked on each day = Quotient of 325 ÷ 5 = 65 Spiral Review Question 3. Mort makes beaded necklaces that he sells for$32 each. About how much will Mort make if he sells 36 necklaces at the local art fair?
Options:
a. $120 b.$900
c. $1,200 d.$1,600

Answer: c. $1,200 Explanation: Cost of each beaded necklace =$32
Number of necklaces = 36
The total cost of the necklaces = $32 x 36 =$1,200 (approx)

Question 4.
Which is the best estimate of 54 × 68?
Options:
a. 4,200
b. 3,500
c. 3,000
d. 350

Explanation:

Taking the terms nearest to the 54 x 68 as 54 x 65 = 3510 = 3500 (approx)

Question 5.
Ms. Eisner pays $888 for 6 nights in a hotel. How much does Ms. Eisner pay per night? Options: a.$5,328
b. $882 c.$148
d. $114 Answer: c.$148

Explanation:
Total pays of Ms Eisner in a hotel = $888 Number of nights = 6 Amount Ms Eisner pay per night =$888 ÷ 6 = $148 Question 6. Which division problem does the model show? Options: a. 42 ÷ 3 b. 44 ÷3 c. 51 ÷ 3 d. 54 ÷ 3 Answer: d. 54 ÷ 3 Explanation: Number of counters in each model = 18 Number of models = 3 Total number of counters = 18 x 3 = 54 Therefore the model displays = 54 ÷ 3 ### Page No. 261 Question 1. Ollie used 852 beads to make 4 bracelets. He put the same number of beads on each bracelet. How many beads does each bracelet have? Check your answer. Divide Check 2 4)$$\overline { 852 }$$ So, each bracelet has _____ beads. _____ beads Answer: 213 Explanation: Total number of beads =852 Number of bracelets = 4 Number of beads in each bracelet = 852 ÷ 4 = 213 Divide and check. Question 2. 2)$$\overline { 394 }$$ _____ Answer: 197 Explanation: STEP 1 Use place value to place the first digit. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the hundreds. STEP 3 Divide the tens. STEP 4 Divide the ones. Question 3. 2)$$\overline { 803 }$$ _____ R _____ Answer: 401 R 1 Explanation: STEP 1 Use place value to place the first digit. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the hundreds. STEP 3 Divide the tens. STEP 4 Divide the ones. Question 4. 3)$$\overline { 3,448 }$$ _____ R _____ Answer: 1149 R 1 Explanation: STEP 1 Use place value to place the first digit. Look at the thousands in 3,448. 3 thousand can be shared among 3 groups without regrouping. The first digit of the quotient will be in the thousands place. STEP 2 Divide the thousands. STEP 3 Divide the hundreds. STEP 4 Divide the tens. STEP 5 Divide the ones. Question 5. 2)$$\overline { 816 }$$ _____ Answer: 408 Explanation: STEP 1 Use place value to place the first digit. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the hundreds. STEP 3 Divide the tens. STEP 4 Divide the ones. Question 6. 4)$$\overline { 709 }$$ _____ R _____ Answer: 177 R 1 Explanation: STEP 1 Use place value to place the first digit. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the hundreds. STEP 3 Divide the tens. STEP 4 Divide the ones. Question 7. 3)$$\overline { 267 }$$ _____ Answer: 89 Explanation: STEP 1 Use place value to place the first digit. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the hundreds. STEP 3 Divide the tens. STEP 4 Divide the ones. Question 8. The flower shop received a shipment of 248 pink roses and 256 red roses. The shop owner uses 6 roses to make one arrangement. How many arrangements can the shop owner make if he uses all the roses? _____ arrangement Answer: 84 arrangements Explanation: Number of pink roses = 248 Number of red roses = 256 Total number of roses = 504 Number of roses in each arrangement = 6 Number of arrangements = 504 ÷ 6 = 84 ### Page No. 262 Use the table for 9–11. Question 9. Four teachers bought 10 origami books and 100 packs of origami paper for their classrooms. They will share the cost of the items equally. How much should each teacher pay? _____$

Answer: $210 Explanation: Number of origami books = 10 Cost of each origami book =$24
Total cost of origami books = $24 x 10 =$240
Number of origami papers = 100
Cost of each origami book = $6 Total cost of origami books =$6 x 100 = $600 Total cost of items =$240 + $600 =$840
Number of teachers = 4
Cost earned by each teacher = $840 ÷ 4 =$210

Question 10.
Communicate Six students shared equally the cost of 18 of one of the items in the chart. Each student paid $24. What item did they buy? Explain how you found your answer. __________ Answer: The students bought origami kit. Explanation: Number of students = 6 Number of items they bought = 18 Amount each student paid =$24
The total amount paid = $24 x 6 =$144
The item they bought can be found by knowing the cost of the item:
Cost of the item=
The total amount paid ÷ Number of items =  144 ÷ 18 = $8 Therefore the item is origami kit. Question 11. Ms Alvarez has$1,482 to spend on origami paper. How many packs can she buy?
_____ packs

Explanation:
Cost of origami paper = $6 Amount Ms Alvarez was supposed to spend on origami paper =$1,482
Number of packs bought = $1,482 ÷$6 = 247

### Common Core – Page No. 263

Divide by 1-Digit Numbers

Divide and check.

Question 1.
318
2)$$\overline { 636 }$$ 318
-6       × 2
——   ——-
03    636
-2
——
16
-16
——-
0

Explanation:
STEP 1 Use place value to place the first digit.  The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the hundreds.
STEP 3 Divide the tens.
STEP 4 Divide the ones.

Question 2.
4)$$\overline { 631 }$$
_____ R _____

Explanation:
STEP 1 Use place value to place the first digit.  The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the hundreds.
STEP 3 Divide the tens.
STEP 4 Divide the ones.

Question 3.
8)$$\overline { 906 }$$
_____ R _____

Explanation:
STEP 1 Use place value to place the first digit.  The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the hundreds.
STEP 3 Divide the tens.
STEP 4 Divide the ones.

Question 4.
6)$$\overline { 6,739 }$$
_____ R _____

Explanation:
STEP 1 Use place value to place the first digit. Look at the thousands in 6,739. 6 thousand can be shared among 6 groups without regrouping. The first digit of the quotient will be in the thousand’s place.
STEP 2 Divide the thousands.
STEP 3 Divide the hundreds.
STEP 4 Divide the tens.
STEP 5 Divide the ones.

Question 5.
4)$$\overline { 2,328 }$$
_____ R _____

Explanation:
STEP 1 Use place value to place the first digit. Look at the thousands in 2,328. 2 thousand can be shared among 4 groups without regrouping. The first digit of the quotient will be in the thousands place.
STEP 2 Divide the thousands.
STEP 3 Divide the hundreds.
STEP 4 Divide the tens.
STEP 5 Divide the ones.

Question 6.
5)$$\overline { 7,549 }$$
_____ R _____

Explanation:
STEP 1 Use place value to place the first digit. Look at the thousands in 7,549. 7 thousand can be shared among 5 groups without regrouping. The first digit of the quotient will be in the thousands place.
STEP 2 Divide the thousands.
STEP 3 Divide the hundreds.
STEP 4 Divide the tens.
STEP 5 Divide the ones.

Problem Solving

Use the table for 7 and 8.

Question 7.
The Briggs rented a car for 5 weeks. What was the cost of their rental car per week?
$_____ Answer:$197

Explanation:
Cost of the car of Briggs = $985 Number of weeks = 5 Cost of rent per week =$985 ÷ 5 =$197 Question 8. The Lees rented a car for 4 weeks. The Santos rented a car for 2 weeks. Whose weekly rental cost was lower? Explain. The rental cost of _____ Answer: Weekly rental cost was lower for Lees compared to Santos Explanation: Cost of the car of Lees =$632
Number of weeks = 4
Cost of rent per week = $632 ÷ 4 =$ 158

Cost of the car of Santos = $328 Number of weeks = 2 Cost of rent per week =$328 ÷ 2 =$164 Therefore weekly rental cost was lower for Lees compared to Santos. ### Common Core – Page No. 264 Lesson Check Question 1. Which expression can be used to check the quotient 646 ÷ 3? Options: a. (251 × 3) + 1 b. (215 × 3) + 2 c. (215 × 3) + 1 d. 646 × 3 Answer: c. (215 × 3) + 1 Explanation: Multiply 215 x 3 = 645 Then add 1 to 645 Then the dividend is 645 + 1 = 646 Question 2. There are 8 volunteers at the telethon. The goal for the evening is to raise$952. If each volunteer raises the same amount, what is the minimum amount each needs to raise to meet the goal?
Options:
a. $7,616 b.$944
c. $119 d.$106

Answer: a. $7,616 Explanation: Number of volunteers = 8 Amount raised by each volunteer =$952
Total amount raised = $952 x 8 =$7,616

Spiral Review

Question 3.
Which product is shown by the model?

Options:
a. 5 × 15 = 75
b. 5 × 16 = 80
c. 5 × 17 = 75
d. 5 × 17 = 85

Answer: d. 5 × 17 = 85

Explanation:
By counting the number of counters we can give the expression.
Number of counters in one row = 17
Number of rows = 5
Therefore the expression = 5 × 17 = 85

Question 4.
The computer lab at a high school ordered 26 packages of CDs. There were 50 CDs in each package. How many CDs did the computer lab order?
Options:
a. 1,330
b. 1,300
c. 1,030
d. 130

Explanation:
Number of packages = 26
Number of CDs in each pack = 50
Total number of CDs the computer lab ordered = 26 x 50 = 1,300

Question 5.
Which of the following division problems has a quotient with the first digit in the hundreds place?
Options:
a. 892 ÷ 9
b. 644 ÷ 8
c. 429 ÷ 5
d. 306 ÷ 2

Explanation:
Use place value to place the first digit. Look at the hundreds in 306. 300 hundred can be shared among 2 groups
without regrouping.
Now there is 30 tens and 6 ones to share among 2 groups.
The first digit of the quotient will be in the hundreds place.

Question 6.
Sharon has 64 ounces of juice. She is going to use the juice to fill as many 6-ounce glasses as possible. She will drink the leftover juice. How much juice will Sharon drink?
Options:
a. 4 ounces
b. 6 ounces
c. 10 ounces
d. 12 ounces

Explanation:
The total quantity of juice = 64 ounces
Quantity of juice she filled = 6 ounces
Quantity of juice she drank = Remainder of 64 ÷  6 = 4

### Page No. 267

Question 1.
A firehouse pantry has 52 cans of vegetables and 74 cans of soup. Each shelf holds 9 cans. What is the least number of shelves needed for all the cans?
First, draw a bar model for the total number of cans.
Next, add to find the total number of cans.
Then, draw a bar model to show the number of shelves needed.
Finally, divide to find the number of shelves needed.
So, _______ shelves are needed to hold all of the cans.
_______ shelves

Explanation:
Number of vegetable cans = 52

Number of soup cans = 74

Total number of cans = 74 +52 = 126
126 ÷ 9 = 14

So, 14 shelves are needed to hold all of the cans.

Question 2.
What if 18 cans fit on a shelf? What is the least number of shelves needed? Describe how your answer would be different.
_______ shelves

Explanation:
Total number of cans = 126
Number of cans which can fit in one shelf = 18
Number of shelves required to place all the cans = 126 ÷ 18 = 7 shelves

### Page No. 268

Question 5.
Ms Johnson bought 6 bags of balloons. Each bag has 25 balloons. She fills all the balloons and puts 5 balloons in each bunch. How many bunches can she make?
_______ bunches

Explanation:
Number of bags = 6
Number of ballons in each bag = 25
Total number of ballons = 25 x 6 = 150
Number of ballons in each bunch = 5
Number of bunches = Total number of ballons ÷ Number of ballons in each bunch = 150 ÷ 5 = 30

Question 6.
An adult’s dinner costs $8. A family of 2 adults and 2 children pays$26 for their dinners. How much does a child’s dinner cost? Explain.
$_______ Answer:$10

Explanation:
Number of children = 2
Cost of dinner of an adult = $8 The total cost of dinner of the adults =$8 x 2 = $16 Total amount paid =$26
Amount spent on children dinner = $26 –$16 = $10 Cost of dinner for the diner =$10 ÷ 2 = $5 Question 9. Ryan bought 8 dozen bandages for the track team first-aid kit. The bandages were divided equally into 4 boxes. How many bandages are in each box? _______ bandages Answer: 24 Explanation: Number of bandages bought for the track team first-aid kit = 8 dozens x 12 = 96 Number of boxes = 4 Number of bandages in each box = 96 ÷ 4 = 24 ### Common Core – Page No. 269 Problem Solving Multistep Division Problems Solve. Draw a diagram to help you. Question 1. There are 3 trays of eggs. Each tray holds 30 eggs. How many people can be served if each person eats 2 eggs? Think: What do I need to find? How can I draw a diagram to help? 45 people can be served Answer: 45 people can be served. Explanation: Drawbar models to visualize the information given. First, draw the model and compare to find the number of eggs they had. Then we must model and divide to find how many eggs are served to each person. Question 2. There are 8 pencils in a package. How many packages will be needed for 28 children if each child gets 4 pencils? ________ packages Answer: 14 packages Explanation: Number of pencils in each package = 8 Number of children = 28 Number of pencils each child needs = 4 Total number of pencils = 28 x 4 =112 Number of packages = 112 ÷ 8 = 14 Question 3. There are 3 boxes of tangerines. Each box has 93 tangerines. The tangerines will be divided equally among 9 classrooms. How many tangerines will each classroom get? ________ tangerines Answer:31 Explanation: Number of boxes = 3 Number of tangerines in each box = 93 Total number of tangerines = 93 x 3 = 279 Number of classrooms = 9 Number of tangerines in each classroom = 279 ÷ 9 = 31 Question 4. Misty has 84 photos from her vacation and 48 photos from a class outing. She wants to put all the photos in an album with 4 photos on each page. How many pages does she need? ______ pages Answer: 33 Explanation: Number of photos from her vacation = 84 Number of photos from her class outing = 48 Total number of photos = 84 + 48 = 132 Number of photos in each page = 4 Number of pages required = 132 ÷ 4 = 33 ### Common Core – Page No. 270 Lesson Check Question 1. Gavin buys 89 blue pansies and 86 yellow pansies. He will plant the flowers in 5 rows with an equal number of plants in each row. How many plants will be in each row? Options: a. 875 b. 175 c. 35 d. 3 Answer: c. 35 Explanation: Number of blue pansies = 89 Number of yellow pansies = 86 Total number of pansies = 89 + 86 = 175 Number of rows = 5 Number of plants in each row = 175 ÷ 5 = 35 Question 2. A pet store receives 7 boxes of cat food. Each box has 48 cans. The store wants to store the cans in equal stacks of 8 cans. How many stacks can be formed? Options: a. 8 b. 42 c. 56 d. 336 Answer: b. 42 Explanation: Number of boxes of cat food = 7 Number of cans in a box = 48 Total number of cans = 48 x 7 = 336 Number of cans in each stack = 8 Number of stacks = 336 ÷ 8 = 42 Spiral Review Question 3. What product does the model show? Options: a. 284 b. 304 c. 340 d. 364 Answer: d. 364 Explanation: Length = 20 +6 = 26 Breadth = 10 + 4 = 14 Area of the rectangle = 26 x 14 = 364 Question 4. Mr. Hatch bought 4 round-trip airplane tickets for$417 each. He also paid $50 in baggage fees. How much did Mr. Hatch spend? Options: a.$467
b. $1,698 c.$1,718
d. $16,478 Answer: c.$1,718

Explanation:
Cost of each ticket of the airplane = $417 Cost baggage fees =$50
Number of trips of the airplane = 5
Cost of the trips = $417 x 5 =$1,668
Type below:
________

Explanation:

### Page No. 282

Question 13.
Carmen has 18 connecting cubes. She wants to model a house shaped like a rectangle. If the model has a height of one connecting cube, how many different ways can Carmen model the house using all 18 connecting cubes?

a. What do you need to know?
Type below:
________

Explanation:

Question 13.
b. How is finding the number of ways to model a rectangular house related to finding factor pairs?
Type below:
________

Explanation:

Question 13.
c. Why is finding the factor pairs only the first step in solving the problem?
Type below:
________

Explanation:

Question 13.
d. Show the steps you used to solve the problem.
Type below:
________

Explanation:

Question 13.
Complete the sentences. Factor pairs for 18 are ___________________ .
There are ______ different ways Carmen can arrange the cubes to model the house.
Type below:
________

Explanation:

Question 14.
Sarah was organizing vocabulary words using index cards. She arranged 40 index cards in the shape of a rectangle on a poster. For 14a–14e, choose Yes or No to tell whether a possible arrangement of cards is shown.
a. 4 rows of 10 cards
i. yes
ii. no

Explanation:

Question 14.
b. 6 rows of 8 cards
i. yes
ii. no

Explanation:

Question 14.
c. 20 rows of 2 cards
i. yes
ii. no

Explanation:

Question 14.
d. 40 rows of 1 card
i. yes
ii. no

Explanation:

Question 14.
e. 35 rows of 5 cards
i. yes
ii. no

Explanation:

Conclusion:

I think the answers provided in the Go Math Grade 4 Answer Key Chapter 4 Divide by 1-Digit Numbers are beneficial for all the students of 4th grade. Our aim is to help the students to become masters in maths. So, Refer to our HMH Go Math 4th Grade Answer Key Chapter 4 Divide by 1-Digit Numbers and secure good marks in the exams.

## Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers

Are you seeing everywhere to find Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers in pdf? If so, you have stepped onto the right page. On this page, we have compiled a pdf formatted HMH Go Math Grade 4 Chapter 3 Multiply 2-Digit Numbers Answer Key. Take the help of the Go Math Grade 4 Solution Key during your practice sessions and clear your queries. Assess your preparation standards and concentrate on the areas you are flagging.

## Go Math Grade 4 Solution Key Pdf Chapter 3 Multiply 2-Digit Numbers

With the help of HMH Go Math Grade 4 Answer Key Ch 3, you can learn the easy methods to solve problems. Answer Key for HMH Go Math Grade 4 Chapter 3 Multiply 2-Digit Numbers consists of all the questions from practice tests, exercises, assessments tests. You guys are recommended to solve the 4th grade Go Math Answers of Chapter 3 Multiply 2-Digit Numbers regularly & attempt the exams with confidence. The topics covered in the Go Math HMH grade 4 Solutions are designed perfectly & in an understandable way.

Lesson 1: Multiply by Tens

Lesson 2: Estimate Products

Lesson 3: Investigate • Area Models and Partial Products

Lesson 4: Multiply Using Partial Products

Mid-Chapter Checkpoint

Lesson 5: Multiply with Regrouping

Lesson 6: Choose a Multiplication Method

Lesson 7: Problem Solving • Multiply 2-Digit Numbers

Review/Test

### Common Core – Page No. 149

Multiply by Tens

Choose a method. Then find the product.

Question 1.
16 × 60 = 960
Use the halving-and-doubling strategy.
Find half of 16: 16 ÷ 2 = 8.
Multiply this number by 60: 8 × 60 = 480
Double this result: 2 × 480 = 960

960

Explanation:
Use the halving-and-doubling strategy.
Find half of 16: 16 ÷ 2 = 8.
Multiply this number by 60: 8 × 60 = 480
Double this result: 2 × 480 = 960

Question 2.
80 × 22 = ______

1760

Explanation:
By using the place value method, Multiply 80 x 22
You can think of 80 as 8 tens
80 x 22 = (22 x 8) tens
= 176 tens
= 176 x 10 = 1760
80 x 22 = 1760

Question 3.
30 × 52 = ______

1560

Explanation:
Use the Associative Property
You can think of 30 as 3 x 10
30 x 52 = (3 x 10) x 52
= 3 x (10 x 52)
=  3 x 520
= 1560
30 x 52 = 1560

Question 4.
60 × 20 = ______

1200

Explanation:
60 x 20
Use the halving and doubling strategy
half of the 60 to make the problem simpler
60/ 2 = 30
Multiply 30 with 20
30 x 20 = 600
Double the 600
2 x 600= 1200
60 x 20 = 1200

Question 7.
31 × 50 = ______

1,550

Explanation:
Use the place value method to multiply 31 x 50
You can think of 50 as 5 tens
31 x 50 = 31 x 5 tens
= 155 tens
= 1,550
31 x 50 = 1,550

Problem Solving

### Common Core – Page No. 150

Lesson Check

Question 1.
For the school play, 40 rows of chairs are set up. There are 22 chairs in each row. How many chairs are there in all?
Options:
a. 800
b. 840
c. 880
d. 8,800

c. 880

Explanation:
As per the given data
For the school play, 40 rows of chairs are available. 22 chairs are available in each row.
Then total chairs in school play are = 22 x 40
By using the place value method
You can think of 40 as 4 tens
22 x 40 = 22 x 4 tens
= 88 tens
= 880
Total chairs in school are = 880

Question 2.
At West School, there are 20 classrooms. Each classroom has 20 students. How many students are at West School?
Options:
a. 40
b. 400
c. 440
d. 4,000

b. 400

Explanation:
From the given data,
Total classrooms in west school = 20
Number of students per each classroom = 20
Then, total students at West School = 20 x 20
By using the associative property
You can think of 20 as 2 x 10
20 x 20 = 20 x (2 x 10)
= (20 x 2) x 10
=(40) x 10
=400
Total number of students at West School = 400

Spiral Review

Question 3.
Alex has 48 stickers. This is 6 times the number of stickers Max has. How many stickers does Max have?
Options:
a. 6
b. 7
c. 8
d. 9

c. 8

Explanation:
As per the give data,
Alex has 48 stickers
That means, X= 48
This is 6 times the number of stickers max has = Y = 6X = 48
Then, number of stickers with Max = Y = X = 48/6 = 8
Number of stickers with Max = Y = 8 Stickers.

Question 4.
Ali’s dog weighs 8 times as much as her cat. Together, the two pets weigh 54 pounds. How much does Ali’s dog weigh?
Options:
a. 6 pounds
b. 42 pounds
c. 46 pounds
d. 48 pounds

d. 48 pounds

Explanation:
From the given data,
Ali’s cat weight = X
Ali’s dog weight = 8 times as much as Ali’s cat = 8X
Together, the two pets weight = (X+8X) = 54 pounds
= 9X = 54 pounds
= X = 54/9 pounds = 6 pounds
Then, Ali’s dog weight = 8X =8 x 6 = 48 pounds.

Question 5.
Allison has 3 containers with 25 crayons in each. She also has 4 boxes of markers with 12 markers in each box. She gives 10 crayons to a friend. How many crayons and markers does Allison have now?
Options:
a. 34
b. 113
c. 123
d. 133

b. 113

Explanation:
As per the given data,
Allison has 3 containers with 25 crayons in each = X = 3 x 25 = 75
Allison has 4 boxes of markers with 12 markers in each box = Y = 4 x 12 = 48
Allison gives 10 crayons to a friend = Z = 75-10 = 65
Now, total number of crayons and markers with Allison = Y + Z = 48 + 65 = 113

Question 6.
The state of Utah covers 82,144 square miles. The state of Montana covers 145,552 square miles. What is the total area of the two states?
Options:
a. 63,408 square miles
b. 223,408 square miles
c. 227,696 square miles
d. 966,992 square miles

c. 227,696 square miles

Explanation:
From the given data,
The state of Utah covers 82,144 square miles
The state of Montana covers 145,552 square miles
Then, Total area of the two states = 82,144 + 145,552
The total area of two states = 227,696 square miles.

### Page No. 153

Question 1.
To estimate the product of 62 and 28 by rounding, how would you round the factors? What would the estimated product be?

1800

Explanation:
By using rounding and mental math
Estimate 62 x 28
Firstly, round each factor
62 x 28

60 x 30
Use mental math
6 x 3 = 18
60 x 30 = 1800
So, estimated product of 62 and 28 = 1800

Estimate the product. Choose a method.

Question 2.
96 × 34
Estimate: _____

3000

Explanation:
Use mental math and compatible numbers
96 x 34

100 x 30
Use mental math
1 x 30 = 30
100 x 30= 3000

Question 3.
47 × $39 Estimate:$ _____

2000

Explanation:
Round to the nearest ten
47 x $39 50 x$40
50 x $4 =$200
50 x $40 = 2000 Question 4. 78 × 72 Estimate: _____ Answer: 5600 Explanation: Use rounding and mental math Round each factor 78 x 72 80 x 70 Use mental math 8 x 7 = 56 80 x 70 = 5600 Practice: Copy and Solve Estimate the product. Choose a method. Question 8. 61 × 31 Estimate: _____ Answer: 1800 Explanation: Round to the nearest ten 61 x 31 60 x 30 = 1800 Question 9. 52 × 68 Estimate: _____ Answer: 3500 Explanation: Round each factor 52 x 68 50 x 70 Use mental math 5 x 7 =35 50 x 70 = 3500 Question 10. 26 × 44 Estimate: _____ Answer: 1200 Explanation: Round to the nearest tens 26 x 44 30 x 40 = 1200 Question 11. 57 ×$69
Estimate: $_____ Answer:$4200

Explanation:
Round each factor
57 x $69 60 x$70
Use mental math
6 x $7 =$42
60 x $70 =$4200

Find two possible factors for the estimated product.

Question 14.
5,600
Type below:
___________

5,600

Explanation:
Let us consider 7 x 8 = 56
70 x 80 = 5,600

Question 15.
2,400
Type below:
___________

2,400

Explanation:
Let us take 4 x 6 = 24
40 x 60 = 2400
Or 3 x 8 = 24
30 x 80 = 2,400

Question 16.
Mr. Parker jogs for 35 minutes each day. He jogs 5 days in week 1, 6 days in week 2, and 7 days in week 3. About how many minutes does he jog?

Explanation:
From the given data,
Mr. Parker jogs per day = 35 minutes
He jogs 5 days in week 1 = 5 x 35 = 175 minutes
6 days in week 2 = 6 x 35 = 210 minutes
7 days in week 3 = 7 x 35 = 245 minutes
Total minutes of jog by Mr. Parker = week 1 + week 2 + week 3
= 175 + 210 + 245
= 630 minutes
So, total minutes of jog by Mr. Parker = 630 minutes

Question 17.
There are 48 beads in a package. Candice bought 4 packages of blue, 9 packages of gold, 6 packages of red, and 2 packages of silver beads. About how many beads did Candice buy?

Explanation:
As per the given data,
48 beads are there in a package
Candice bought 4 packages of blue beads = 4 x 48 = 192
9 packages of gold beads = 9 x 48 = 432
6 packages of red beads = 6 x 48 = 288
2 packages of silver beads = 2 x 48 = 96
Total beads bought by Candice = 192 + 432 + 288 + 96
So, total beads bought by Candice = 1008.

### Page No. 154

Question 20.
If Mel opens his refrigerator door 36 times every day, how many times will it be opened in April? Will the exact answer be more than or less than the estimate? Explain.
Type below:
___________

1200

Explanation:
From the given data,
Mel opens his refrigerator door per day = 36 times
Number of days in April month = 30 days
Refrigerator door opened in April month = 36 * 30
Round the factors
36 x 30

40 x 30 = 1200

Question 21.
Represent a Problem What question could you write for this answer? The estimated product of two numbers, which are not multiples of ten, is 2,800.
Type below:
___________

2800

Explanation:
Let us take
1.
38 × 21
↓        ↓
40 × 20 = 800
2,800 = 42 x 68
↓    ↓
40 x  70 = 2800

Question 22.
Which is a reasonable estimate for the product? Write the estimate. An estimate may be used more than once.

26 × 48 __________
28 × 21 __________
21 × 22 __________
51 × 26 __________

25 x 50 = 1250
30 x 20 = 600
20 x 20 = 400
50 x 25 = 1250

Explanation:
26 x 48 -> 25 x 50 = 1250
28 x 21 -> 30 x 20 = 600
21 x 22 -> 20 x 20 = 400
51 x 26 -> 50 x 25 = 1250

### Common Core – Page No. 155

Estimate Products
Estimate the product. Choose a method.

Question 1.
38 × 21
38 × 21
↓       ↓
40 × 20
800

800

Explanation:
38 × 21
↓        ↓
40 × 20
800

Question 2.
63 × 19
Estimate: _____

1200

Explanation:
63 x 19

60 x 20 = 1200
Estimated product of 63 x 19 = 1200

Question 5.
37 × $44 Estimate:$ _____

$1600 Explanation: 37 ×$44

40 x $40 =$1600
Estimated Product of 37 x $44 =$1600

Question 6.
85 × 71
Estimate: _____

6300

Explanation:
85 × 71

90 x 70 = 6300
Estimated Product of 85 x 71 = 6300

Question 7.
88 × 56
Estimate: _____

4950

Explanation:
88 × 56

90 x 55 = 4950
Estimated Product of 90 x 55 = 4950

Question 8.
97 × 13
Estimate: _____

1,000

Explanation:
97 × 13

100 x 10 = 1,000

Question 9.
92 × 64
Estimate: _____

5850

Explanation:
92 × 64

90 x 65 = 5850

Problem Solving

### Common Core – Page No. 156

Lesson Check

Question 1.
Which is the best estimate for the product
43 × 68?
Options:
a. 3,500
b. 2,800
c. 2,400
d. 280

b. 2,800

Explanation:
Round to the nearest tens
43 x 68

40 x 70
Use mental math
4 x 7 = 28
40 x 70 = 2800
Estimated product of 43 x 68 = 2800

Question 2.
Marissa burns 93 calories each time she plays fetch with her dog. She plays fetch with her dog once a day. About how many calories will Marissa burn playing fetch with her dog in 28 days?
Options:
a. 4,000
b. 2,700
c. 2,000
d. 270

b. 2,700

Explanation:
From the given data,
Marissa burned calories each time when she plays fetch with her dog= 93 calories
Then, Marissa burned calories in 28 days while playing fetch with her dog = 28 x 93
Round to the nearest tens
28 x 93

30 x 90
Then, estimated burned calories in 28 days by Marissa = 2700 calories

Spiral Review

Question 3.
Use the model to find 3 × 126.

Options:
a. 368
b. 378
c. 468
d. 478

b. 378

Explanation:
From the above Figure,
3 x 126 = 3 x 100 + 3 x 20 + 3 x 6
= 300 + 60 + 18
= 378
3 x 126 = 378

Question 4.
A store sells a certain brand of jeans for $38. One day, the store sold 6 pairs of jeans of that brand. How much money did the store make from selling the 6 pairs of jeans? Options: a.$188
b. $228 c.$248
d. $288 Answer: b.$228

Explanation:
As per the given data,
A store sells a certain brand of jeans for rupees = $38 One day, the store sold 6 pairs of jeans of that brand = 6 x$38
6 x $38 =$228
The total amount of 6 pairs of jeans = $228 Question 5. The Gateway Arch in St. Louis, Missouri, weighs about 20,000 tons. Which amount could be the exact number of tons the Arch weighs? Options: a. 31,093 tons b. 25,812 tons c. 17,246 tons d. 14,096 tons Answer: c. 17,246 tons Explanation: From the given data, The Gateway Arch in St.Louis, Missouri weight = about 20,000 tons From the available options, 17,246 tons is closer to 20,000 tons Then, the exact number of tons the Arch weighs = 17,246 tons Question 6. Which is another name for 23 ten thousands? Options: a. 23,000,000 b. 2,300,000 c. 230,000 d. 23,000 Answer: c. 230,000 Explanation: As per the data, Another name for 23 ten thousands = 23 x 10,000 = 230,000 Another name for 23 ten thousand = 2,30,000 ### Page No. 159 Find the product. Question 1. 16 × 19 16 × 19 = _____ Answer: 304 Explanation: 16 x 19 = 304 Question 2. 18 × 26 18 × 26 = _____ Answer: 468 Explanation: 200 + 160 + 60 + 48 = 468 Question 3. 27 × 39 27 × 39 = ______ Answer: 1,053 Explanation: 600 + 210 + 180 +63 = 1053 Draw a model to represent the product. Then record the product. Question 4. 14 × 16 = ______ Answer: 224 Explanation: 100 + 40 + 60 + 24 = 224 Question 5. 23 × 25 = ______ Answer: 575 Explanation: 400 + 60 + 100 + 15 = 575 Question 6. Explain how modeling partial products can be used to find the products of greater numbers. Type below: __________ Answer: You can use mental math to find the partial products and then find the sum of the partial products. Explanation: Question 7. Emma bought 16 packages of rolls for a party. There were 12 rolls in a package. After the party there were 8 rolls left over. How many rolls were eaten? Explain. ______ rolls Answer: 184 rolls were eaten Explanation: From the given data, Emma bought 16 packages of rolls for a party There were 12 rolls in a package Then, total rolls = 16 x 12 = 192 100 + 60 + 20 + 12 =192 After the party there were 8 rolls left over Then, total eaten rolls are = 192 – 8 = 184 ### Page No. 160 Question 8. Jamal and Kim used different ways to solve 12 × 15 by using partial products. Whose answer makes sense? Whose answer is nonsense? Explain your reasoning. Jamal’s Work 100 + 20 + 10 = 130 Kim’s Work 120 + 60 = 180 a. For the answer that is nonsense, write an answer that makes sense. Type below: __________ Answer: a. Jamal’s work makes nonsense. 100 + 20 + 50 + 10 = 180 it makes sense Question 8. b. Look at Kim’s method. Can you think of another way Kim could use the model to find the product? Explain. Type below: __________ Answer: Other method: 12 x 15 10 x 12 = 120 5 x 12 = 60 120 + 60 = 180. Explanation: Kim follows another method to find 12 x 15 That is, 100 + 50 = 150 20 + 10 = 30 Then, 150 + 30 =180 12 x 15 = 180 Question 9. Look at the model in 8b. How would the partial products change if the product was 22 × 15? Explain why you think the products changed. Type below: __________ Answer: 330 Explanation: Following the 8b method 22 x 15 =330 200 + 100 = 300 20 + 10 = 30 Now, 300 + 30 = 330 Finally, 22 x 15 = 330 The factor of 15 is increased in present problem. So, the product also increases for 15 x 22. ### Common Core – Page No. 161 Area Models and Partial Products Draw a model to represent the product. Then record the product. Question 1. 13 × 42 Answer: Question 2. 18 × 34 = ______ Answer: 300 + 40 + 240 + 32 = 612 Question 3. 22 × 26 = ______ Answer: 400 + 120 + 40 + 12 = 572 Question 4. 1 5 × 33 = ______ Answer: 300 + 30 + 150 + 15 = 495 Question 5. 23 × 29 = ______ Answer: 400 + 180 + 60 + 27 = 667 Question 6. 19 × 36 = ______ Answer: 300 + 60 + 270 + 54 = 684 Problem Solving Question 7. Sebastian made the following model to find the product 17 × 24. Is his model correct? Explain. a. yes b. no Answer: b. no Explanation: 200 + 40 + 140 + 28 = 408 Question 8. Each student in Ms. Sike’s kindergarten class has a box of crayons. Each box has 36 crayons. If there are 18 students in Ms. Sike’s class, how many crayons are there in all? ______ crayons Answer: 648 crayons Explanation: From the given information, Each student in Ms.Sike’s kindergarten class has a box of crayons Crayons in each box = 36 Crayons Number of students in Mr.Sike’s class = 18 students Total crayons = 18 x 36 300 + 60 + 240 + 48 = 648 ### Common Core – Page No. 162 Lesson Check Question 1. Which product does the model below represent? Options: a. 161 b. 230 c. 340 d. 391 Answer: d. 391 Explanation: 200 + 30 + 140 + 21 = 391 17 x 23 = 391 Question 2. Which product does the model below represent? Options: a. 219 b. 225 c. 244 d. 275 Answer: b. 225 Explanation: 130 + 20 + 65 + 10 = 225 15 x 15 = 225 Spiral Review Question 3. Mariah builds a tabletop using square tiles. There are 12 rows of tiles and 30 tiles in each row. How many tiles in all does Mariah use? Options: a. 100 b. 180 c. 360 d. 420 Answer: c. 360 Explanation: From the given data, Mariah builds a tabletop using square tiles Square contains 12 rows of tiles and 30 tiles in each row = 12 x 30 12 x 30 = 360 tiles Total tiles used by Mariah = 360 tiles Question 4. Trevor bakes 8 batches of biscuits, with 14 biscuits in each batch. He sets aside 4 biscuits from each batch for a bake sale and puts the rest in a jar. How many biscuits does Trevor put in the jar? Options: a. 112 b. 80 c. 50 d. 32 Answer: b. 80 Explanation: As per the given data, Number of biscuits baked by Trevor = 8 batches Number of biscuits in each batch = 14 biscuits So, total biscuits = 14 x 8 = 112 Trevor sets aside 4 biscuits from each batch for a bake = 8*4 = 32 biscuits are aside for a bake Trevor kept rest of biscuits in a jar = 112 – 32 = 80 So, 80 biscuits are put in the jar by the Trevor Question 5. Li feeds her dog 3 cups of food each day. About how many cups of food does her dog eat in 28 days? Options: a. 60 cups b. 70 cups c. 80 cups d. 90 cups Answer: c. 80 cups Explanation: As per the given data, Li feeds her dog per day = 3 cups of food Then, Li feeds her dog for 28 days = 3 x 28 = 84 cups of food So, Li feeds her dog with 84 cups of food in 28 days Question 6. Which symbol makes the number sentence true? 4 ■ 0 = 0 Options: a. + b. – c. × d. ÷ Answer: c. × Explanation: 4 x 0 = 0 ### Page No. 165 Question 1. Find 24 × 34. _____ Answer: 816 Explanation: Question 2. 1 2 × 1 2 ——– _____ Answer: 144 Explanation: Question 3. 3 1 × 2 4 ——- _____ Answer: 744 Explanation: Question 4. 2 5 × 4 3 ——- _____ Answer: 1,075 Explanation: Question 5. 3 7 × 2 4 ——- _____ Answer: 888 Explanation: Question 6. 5 4 × 1 5 ——- _____ Answer: 810 Explanation: Question 7. 8 7 × 1 6 ——- _____ Answer: 1,392 Explanation: Question 8. 6 2 × 5 6 ——- _____ Answer: 3,472 Explanation: Question 9. 4 9 × 6 3 ——- _____ Answer: 3,087 Explanation: Practice: Copy and Solve Record the product. Question 10. 38 × 47 _____ Answer: 1,786 Explanation: Question 11. 46 × 27 _____ Answer: 1,242 Explanation: Question 12. 72 × 53 _____ Answer: 3,816 Explanation: Question 13. 98 × 69 _____ Answer: 6,762 Explanation: Question 14. 53 × 68 _____ Answer: 3,604 Explanation: Question 15. 76 × 84 _____ Answer: 6,384 Explanation: Question 16. 92 × 48 _____ Answer: 4,416 Explanation: Question 17. 37 × 79 _____ Answer: 2,923 Explanation: Reason Abstractly Algebra Find the unknown digits. Complete the problem. Question 18. Type below: ___________ Answer: 1,824 Explanation: Question 19. Type below: ___________ Answer: 7,954 Explanation: Question 20. Type below: ___________ Answer: 1,908 Explanation: Question 21. Type below: ___________ Answer: 952 Explanation: ### Page No. 166 Use the picture graph for 22–24. Question 22. Use Graphs A fruit-packing warehouse is shipping 15 boxes of grapefruit to a store in Santa Rosa, California. What is the total weight of the shipment? ______ pounds Answer: 1275 pounds Explanation: From the given data, A fruit packing warehouse is shipping 15 boxes of grapefruit to store in Santa Rose, California Grapefruit weight per box = 85 pounds Total weight of the shipment = 85 x 15 So, the total weight of the shipment = 1275 pounds Question 23. How much less do 13 boxes of tangelos weigh than 18 boxes of tangerines? ______ pounds Answer: 450 pounds Explanation: As per the given data, Tangelos weight per box = 90 pounds Then, the weight of the 13 boxes of tangelos = 90 x 13 And, the weight of the 18 boxes of tangelos = 90 x 18 1620 – 1170 = 450 So, 13 boxes of tangelos weight are 450 pounds less than 18 boxes of tangelos weight Question 24. What is the weight of 12 boxes of oranges? ______ pounds Answer: 1,080 pounds Explanation: The weight of the oranges per box = 90 pounds then, weight of 12 boxes oranges = 90 x 12 So, weight of 12 boxes oranges = 1,080 pounds Question 25. Each person in the United States eats about 65 fresh apples each year. Based on this estimate, how many apples do 3 families of 4 eat each year? ______ apples Answer: 780 apples Explanation: From the given data, Each person in the united states eats fresh apples per year = 65 3 families of 4 persons = 3 x 4 = 12 persons Then, the number of apples eat by 12 persons = 65 x 12 So, the total number of apples eat by 12 persons per year = 780 Question 26. The product 26 × 93 is greater than 25 × 93. How much greater? Explain how you know without multiplying. ______ Answer: The difference is 93 26 x 93 is one more group of 93 than 25 x 93 Question 27. Margot wants to use partial products to find 22 × 17. Write the numbers in the boxes to show 22 × 17. Type below: __________ Answer: Explanation: 22 x 17 (20 + 2) x 17 20 x 17 + 2 x 17 20 x (10 + 7) + 2 x (10 + 7) (20 x 10) + (20 x 7) + (2 x 10) + (2 x 7) ### Common Core – Page No. 167 Multiply Using Partial Products Record the product. Question 1. 2 3 × 7 9 ——— 1, 4 0 0 2 1 0 1 8 0 + 2 7 ——– 1, 8 1 7 Answer: 1, 8 1 7 Explanation: 2 3 × 7 9 ——— 1, 4 0 0 2 1 0 1 8 0 + 2 7 ——– 1, 8 1 7 Question 2. 5 6 × 3 2 ——- _______ Answer: 1,792 Explanation: Question 3. 8 7 × 6 4 ——- _______ Answer: 5,568 Explanation: Question 4. 3 3 × 2 5 ——- _______ Answer: 825 Explanation: Question 5. 9 4 × 1 2 ——- _______ Answer: 1,128 Explanation: Question 6. 5 1 × 7 7 ——- _______ Answer: 3,927 Explanation: Question 7. 6 9 × 4 9 ——- _______ Answer: 3,381 Explanation: Question 8. 8 6 × 8 4 ——- _______ Answer: 7,224 Explanation: Question 9. 9 8 × 4 2 ——- _______ Answer: 4,116 Explanation: Question 10. 7 3 × 3 7 ——- _______ Answer: 2,701 Explanation: Question 11. 8 5 × 5 1 ——- _______ Answer: 4,335 Explanation: Problem Solving Question 12. Evelyn drinks 8 glasses of water a day, which is 56 glasses of water a week. How many glasses of water does she drink in a year? (1 year = 52 weeks) _______ glasses Answer: 2,912 glasses Explanation: As per the given data, Evelyn drinks 8 glasses of water a day Evelyn drinks water per week = 56 glasses Then, the number of glasses per 52 weeks = 52 x 56 Total number of glasses of water drink by Evelyn per year = 2912 glasses of water Question 13. Joe wants to use the Hiking Club’s funds to purchase new walking sticks for each of its 19 members. The sticks cost$26 each. The club has $480. Is this enough money to buy each member a new walking stick? If not, how much more money is needed? Is the money enough? _______ How much more is needed? _______ Answer: This amount is not enough to buy walking sticks Still,$14 amount is needed to buy walking sticks

Explanation:
From the given data,
Joe wants to use the Hiking club funds to purchase new walking sticks for each of its 19 members
Cost per each stick = $26 Total walking sticks cost per 19 members =$26 x 19

Total cost for walking sticks for 19 members = $494 The club has =$480
This amount is not enough to buy walking sticks
Still, $14 amount is needed to buy walking sticks ### Common Core – Page No. 168 Lesson Check Question 1. A carnival snack booth made$76 selling popcorn in one day. It made 22 times as much selling cotton candy. How much money did the snack booth make selling
cotton candy?
Options:
a. $284 b.$304
c. $1,562 d.$1,672

d. $1,672 Explanation: As per the given data, A carnival snack booth made popcorn in one day =$76
It made 22 times as much selling cotton candy
Then, total selling cotton candy made by snack booth = $76 x 22 So,$1672 money snack booth will get for selling cotton candy

Question 2.
What are the partial products of
42 × 28?
Options:
a. 800, 80, 40, 16
b. 800, 16
c. 800, 40, 320, 16
d. 80, 16

c. 800, 40, 320, 16

Explanation:

So, partial products of 42 x 28 are 800, 40, 320, 16

Spiral Review

Question 3.
Last year, the city library collected 117 used books for its shelves. This year, it collected 3 times as many books. How many books did it collect this year?
Options:
a. 832
b. 428
c. 351
d. 72

c. 351

Explanation:
From the given data,
Last year, the number of used books collected by city library by its shelves = 117 books
This year, it collected 3 times as many books = 3 x 117 =351 books
Total number of books collected by the city library for this year = 351 books

Question 4.
Washington Elementary has 232 students. Washington High has 6 times as many students. How many students does Washington High have?
Options:
a. 1,392
b. 1,382
c. 1,292
d. 1,281

a. 1,392

Explanation:
As per the given data,
The number of students in Washington elementary = 232 students
Washington High has 6 times as many students = 6 x 232 = 1392
Total number of students in Washington High = 1392 students

Question 5.
What are the partial products of 35 × 7?
Options:
a. 10, 12
b. 21, 35
c. 210, 35
d. 350, 21

c. 210, 35

Explanation:
Partial products of 35 x 7 are 210, 35

Question 6.
Shelby has ten $5 bills and thirteen$10 bills. How much money does Shelby have in all?
Options:
a. $15 b.$60
c. $63 d.$180

d. $180 Explanation: From the given data, Shelby has ten$5 bills and thirteen $10 bills = (10 x$5) + (13 x $10) = ($50) + ($130) =$180
Total money with Shelby = $180 ### Page No. 169 Question 1. Explain how to find 40 × 50 using mental math. Type below: __________ Answer: 200 Explanation: 40 x 50 By using mental math 4 x 5 = 20 40 x 50 = 200 Question 2. What is the first step in estimating 56 × 27? Type below: __________ Answer: 18 centimeters Explanation: Round to the nearest values. So, the first step of the estimated 56 x 27 is rounding to the nearest value which is 60 x 30 Choose a method. Then find the product. Question 5. 12 × 80 = _____ Answer: 960 Explanation: Use the halving and doubling strategy half of the 80 to make the problem simpler 80/ 2 = 40 Multiply 40 with 12 40*12 = 480 Double the 480 2*480= 960 12*80 = 960 Question 6. 70 × 50 = _____ Answer: 3,500 Explanation: 70 x 50 By using the place value method You can take 50 as 5 tens 70 x 50 = 70 x 5 tens = 350 tens 70 x 50 = 3,500 Question 7. 58 × 40 = _____ Answer: 2,320 Explanation: By using the associative property You can think of 40 as (4 x 10) 58 x 40 = 58 x (4 x 10) = (58 x 4) x 10 = 232 x 10 58 x 40 = 2,320 Question 8. 30 × 40 = _____ Answer: 1,200 Explanation: Use the halving and doubling strategy half of the 40 to make the problem simpler 40/ 2 = 20 Multiply 20 with 30 20*30 = 600 Double the 600 2*600= 1200 30*40 = 1,200 Question 9. 14 × 60 = _____ Answer: 840 Explanation: By using the place value method You can take 60 as 6 tens 14 x 60 = 14 x 6 tens = 84 tens 14 x 60 = 840 Question 10. 20 × 30 = _____ Answer: 600 Explanation: By using the associative property You can think of 30 as (3 x 10) 20 x 30 = 20 x (3 x 10) = (20 x 3) x 10 = 60 x 10 20 x 30 = 600 Question 11. 16 × 90 = _____ Answer: 1,440 Explanation: Use the halving and doubling strategy half of the 90 to make the problem simpler 90/ 2 = 45 Multiply 45 with 16 16*45 = 720 Double the 720 2*720= 1440 16*90 = 1,440 Estimate the product. Choose a method. Question 14. 43 × 25 Estimate: _____ Answer: 1,000 Explanation: Round to the nearest tens. 43 is close to 40; 25 is close to 25; 40 x 25 = 1000 Estimated product of 43 x 25 = 1,000 Question 15. 76 × 45 Estimate: _____ Answer: 3,200 Explanation: Round to the nearest tens. 76 is close to 80; 45 is close to 40; Use the mental math 8 x 4 = 32 80 x 40 = 3200 So, the estimated product of 76 x 45 = 3,200 Question 16. 65 ×$79
Estimate: _____

$4,800 Explanation: Round to the nearest tens. 65 is close to 60;$79 is close to $80; Use the mental math 6 x$8 = $48 60 x$80 = $4800 So, estimated product of 65 x$79 = $4,800 Question 17. 92 × 38 Estimate: _____ Answer: 3,600 Explanation: Round to the nearest tens. 92 is close to 90; 38 is close to 40; Use the mental math, then 9 x 4 = 36 90 x 40 = 3,600 So, estimated product of 92 x 38 = 3,600 Question 18. 37 × 31 Estimate: _____ Answer: 1,200 Explanation: Round to the nearest tens. 37 is close to 40; 31 is close to 30; Use the mental math, then 4 x 3 = 12 40 x 30 = 1,200 So, estimated product of 37 x 31 = 1,200 Question 19. 26 ×$59
Estimate: _____

$1,800 Explanation: Round to the nearest tens. 26 is close to 30;$59 is close to $60; Use the mental math, then 3 x$6 = $18 30 x$60 = $1,800 So, estimated product of 26 x$59 = $1,800 Question 20. 54 × 26 Estimate: _____ Answer: 18 centimeters Explanation: Round to the nearest tens. 54 is close to 50; 26 is close to 30; Use the mental math 5 x 3 = 15 50 x 30 = 1,500 So, estimated product of 54 x 26 = 1,500 Question 21. 52 × 87 Estimate: _____ Answer: 4,500 Explanation: Round to the nearest tens. 52 is close to 50; 87 is close to 90; Use the mental math 5 x 9 = 45 50 x 90 = 4500 So, estimated product of 52 x 87 = 4,500 Question 22. 39 × 27 Estimate: _____ Answer: 18 centimeters Explanation: Round to the nearest tens. 39 is close to 40; 27 is close to 30; Use the mental math 4 x 3 = 12 40 x 30 = 1,200 So, estimated product of 39 x 27 = 1,200 Question 23. 63 × 58 Estimate: _____ Answer: 3,600 Explanation: Round to the nearest tens. 63 is close to 60; 58 is close to 60; Use the mental math 6 x 6 = 36 60 x 60 = 3,600 So, estimated product of 63 x 58 = 3,600 ### Page No. 170 Question 25. Tito wrote the following on the board. What is the unknown number? ______ Answer: 400 Explanation: An unknown number is 50 x 8 = 400 Question 26. What are the partial products that result from multiplying 15 × 32? Type below: __________ Answer: Partial products are 300, 150, 20, 10 Explanation: Partial products are 300, 150, 20, 10 ### Page No. 173 Question 1. Look at the problem. Complete the sentences. Multiply ____ and ____ to get 0. Multiply ____ and ____ to get 1,620. Add the partial products. 0 + 1,620 = ____ _____ Answer: Multiply 27 and 0 to get 0. Multiply 27 and 6 to get 1,620. Add the partial products. 0 + 1,620 = 1,620. Estimate. Then find the product. Question 2. 6 8 × 5 3 ——- Estimate: _________ Product: __________ Answer: Estimate: 3,500 Product: 3,604 Explanation: 68 is closer to 70 and 53 is closer to 50 Estimate: 70 x 50 = 3,500 60 x 53 = 3180 8 x 53 = 424 3180 + 424 = 3604 Product 3,604 Question 3. 6 1 × 5 4 ——- Estimate: _________ Product: __________ Answer: Estimate: 3,000 Product: 3,294 Explanation: 61 is closer to 60 and 54 is closer to 50 Estimate: 60 x 50 = 3,000 60 x 54 = 3240 1 x 54 = 54 3240 + 54 = 3294 Product 3,294 Question 6. 7 8 × 5 6 ——- Estimate: _________ Product: __________ Answer: Estimate: 4,800 Product: 4,368 Explanation: 78 is closer to 80 and 56 is closer to 60 Estimate: 80 x 60 = 4,800 70 x 56 = 3920 8 x 56 = 448 3920 + 448 = 4368 Product 4,368 Question 7. 2 7 × 2 5 ——- Estimate: _________ Product: __________ Answer: Estimate: 600 Product: 675 Explanation: 27 is closer to 30 and 25 is closer to 20 Estimate: 30 x 20 = 600 20 x 25 = 500 7 x 25 = 175 500 + 175 = 675 Product 675 Practice: Copy and Solve Estimate. Then find the product. Question 8. 34 × 65 Estimate: _________ Product: __________ Answer: Estimate: 1,800 Product: 2,210 Explanation: 34 is closer to 30 and 65 is closer to 60 Estimate: 30 x 60 = 1,800 30 x 65 = 1950 4 x 65 = 260 1950 + 260 = 2210 Product 2,210 Question 9. 42 ×$13
Estimate: $_________ Product:$ _________

Estimate: $400 Product:$546

Explanation:
42 is closer to 40 and 13 is closer to 10
Estimate: 40 x 10 = 400
40 x $13 =$520
2 x $13=$26
$520 +$26 = $546 Product$546

Question 10.
60 × 17
Estimate: _________
Product: __________

Estimate: 1,200
Product: 1,020

Explanation:
17 is closer to 20
Estimate: 60 x 20 = 1,200
60 x 17 = 1020
Product = 1,020

Question 11.
62 × 45
Estimate: _________
Product: __________

Estimate: 2,400
Product: 2,790

Explanation:
62 is closer to 60 and 45 is closer to 40
Estimate: 60 x 40 = 2,400
60 x 45 = 2700
2 x 45= 90
2700 + 90 = 2790
Product 2,790

Question 12.
57 × $98 Estimate:$ _________
Product: $_________ Answer: Estimate: 6,000 Product: 5,586 Explanation: 57 is closer to 60 and 98 is closer to 100 Estimate: 60 x 100 = 6,000 50 x 98 = 4900 7 x 98= 686 4900 + 686 = 5586 Product 5,586 Look for a Pattern Algebra Write a rule for the pattern. Use your rule to find the unknown numbers. Question 13. Rule _____________ Type below: _________ Answer: Explanation: 1 hour = 60 min Then, 5hr = 5 x 60 = 300 min 10hr = 10 x 60 = 600 min 15hr = 15 x 60 = 900 min 20hr = 20 x 60 = 1200 min 25hr = 25 x 60 = 1500 min Question 14. Owners of a summer camp are buying new cots for their cabins. There are 16 cabins. Each cabin needs 6 cots. Each cot costs$92. How much will the new cots cost?
$_______ Answer:$8,832

Explanation:
As per the given data,
Owners pf a summer camp are buying new cots for their cabins
Number of cabins = 16
Each cabin needs 6 cots
Then, total cots = 16 x 6 = 96
Each cot cost = $92 Then, cost for total cots =$92 x 96
92 is closer to 90 and 96 is closer to 100
Estimate = 90 x 100 = 9,000
90 x 96 = 8640
2 x 96 = 192
8640 + 192 = 8832
Product = 8,832

### Page No. 174

Question 16.
Machine A can label 11 bottles in 1 minute. Machine B can label 12 bottles in 1 minute. How many bottles can both machines label in 15 minutes?

a. What do you need to know?
Type below:
__________

number of bottles labeled by Machine A and Machine B in 15 minutes

Question 16.
b. What numbers will you use?
Type below:
__________

15x 11 and 15 x 12

Question 16.
c. Tell why you might use more than one operation to solve the problem.
Type below:
__________

To find out the total number of bottle made by both machines A & B

Question 16.
d. Solve the problem.
So, both machines can label ____ bottles in ____ minutes.
Type below:
__________

Machine A can label 11 bottles in 1 minute
Then, the number of bottles labeled by machine A in 15 minutes = 15 x 11 = 165
Machine B can label 12 bottles in 1 minute
Then, number of bottles labelled by Machine B in 15 minutes = 15 x 12 = 180
Total bottles labelled by both the machines in 15 minutes = 165 + 180 = 345

Question 17.
Make Sense of Problems
A toy company makes wooden blocks. A carton holds 85 blocks. How many blocks can 19 cartons hold?
______ blocks

1,615 blocks

Explanation:
From the given data,
A toy company makes wooden blocks
A carton holds 85 blocks
Then, number of blocks hold by 19 cartons = 19 x 85 = 1615
Total number of blocks held by 19 cartons = 1,615

Question 19.
Mr. Garcia’s class raised money for a field trip to the zoo. There are 23 students in his class. The cost of the trip will be $17 for each student. What is the cost for all the students? Explain how you found your answer.$ ______

$391 Explanation: As per the given data, Mr. Garcia’s class raised money for a field trip to the zoo Total number of students in his class = 23 students Cost of the trip for each student =$17
Then, total cost for all the students = $17 x 23 =$391

### Common Core – Page No. 175

Multiply with Regrouping
Estimate. Then find the product.

Question 1.
Estimate: 2,700
Think: 87 is close to 90 and 32 is close to 30.
90 × 30 = 2,700

2,784

Explanation:
Think: 87 is close to 90 and 32 is close to 30.
90 × 30 = 2,700

Question 2.
7 3
× 2 8
——–
Estimate: ______
Product: _______

Estimate: 2,100
Product: 2,044

Explanation:
Estimate: 73 is close to 70; 28 is close to 30.
So, 70 x 30 = 2,100.
Product: Write 73 as 7 tens and 3 ones. Multiply 28 by 3 ones.
2
28
x 73
——–
84 <– 3 x 28
Multiply 28 by 7 tens
5
28
x 73
——–
1960 <– 70 x 28
84 + 1960 = 2,044.
So, 73 x 28 = 2,044.

Question 3.
4 8
× 3 8
——–
Estimate: ______
Product: _______

Estimate: 2,000
Product: 1,824

Explanation:
48 is close to 50 and 38 is close to 40.
Estimate: 50 × 40 = 2,000
40 x 38 = 1520
8 x 38 = 304
1520 + 304 = 1824.
Product: 1,824

Question 4.
5 9
× 5 2
——–
Estimate: ______
Product: _______

Estimate: 3,000
Product: 3,068

Explanation:
59 is close to 60 and 52 is close to 50.
Estimate: 60 × 50 = 3,000
50 x 52 = 2600
9 x 52 = 468
2600 + 468 = 3068.
Product: 3,068.

Question 7.
9 1
× 1 9
——–
Estimate: ______
Product: _______

Estimate: 1,800
Product: 1,729

Explanation:
91 is close to 90 and 19 is close to 20.
Estimate: 90 × 20 = 1,800
90 x 19 = 1,710
1 x 19 = 19
1,710+ 19 = 1,729.
Product: 1,729.

Problem Solving

Question 8.
Baseballs come in cartons of 84 baseballs. A team orders 18 cartons of baseballs. How many baseballs does the team order?
_______ baseballs

1,512 baseballs

Explanation:
To find total baseballs, 84 x 18
80 x 18 = 1,440
4 x 18 = 72
84 x 18 = 1,512

Question 9.
There are 16 tables in the school lunchroom. Each table can seat 22 students. How many students can be seated at lunch at one time?
_______ students

352 students

Explanation:
Total Students = 16 x 22
10 x 22 = 220
6 x 22 = 132
220 + 132 = 352.
352 students can be seated at lunch at one time

### Common Core – Page No. 176

Lesson Check

Question 1.
The art teacher has 48 boxes of crayons. There are 64 crayons in each box. Which is the best estimate of the number of crayons the art teacher has?
Options:
a. 2,400
b. 2,800
c. 3,000
d. 3,500

c. 3,000

Explanation:
1. Total number of crayons = 48 x 64
48 is close to 50; 64 is close to 60
50 x 60 = 3,000.
The art teacher has about to 3, 000 crayons.

Question 2.
A basketball team scored an average of 52 points in each of 15 games. How many points did the team score in all?
Options:
a. 500
b. 312
c. 780
d. 1,000

c. 780

Explanation:
Total Points = 52 x 15
50 x 15 = 750
2 x 15 = 30
750 + 30 = 780.
The basketball team scored 780 points in total.

Spiral Review

Question 3.
On Saturday, an orchard sold 83 bags of apples. There are 27 apples in each bag. Which expression represents the total number of apples sold?
Options:
a. 16 + 6 + 56 + 21
b. 160 + 60 + 56 + 21
c. 160 + 60 + 560 + 21
d. 1,600 + 60 + 560 + 21

d. 1,600 + 60 + 560 + 21

Explanation:
Total number of apples sold = 83 x 27
80 x 27 = 2,160
3 x 27 = 81
2,160 + 81 = 2,241.
The total number of apples sold = 2,241.
16 + 6 + 56 + 21 = 99 not equal to 2,241
160 + 60 + 56 + 21 = 297 not equal to 2,241
160 + 60 + 560 + 21 = 801 not equal to 2,241
1,600 + 60 + 560 + 21 = 2,241 equal to 2,241
1,600 + 60 + 560 + 21 = 2,241 is correct.

Question 4.
Hannah has a grid of squares that has 12 rows with 15 squares in each row. She colors 5 rows of 8 squares in the middle of the grid blue. She colors the rest of
the squares red. How many squares does Hannah color red?
Options:
a. 40
b. 140
c. 180
d. 220

b. 140

Explanation:
Hannah has a grid of squares that has 12 rows with 15 squares in each row = 12 x 15 = 180.
The grid of squares in blue = 5 x 8 = 40.
The grid of squares in red = 180 – 40 = 140.

Question 5.
Gabriella has 4 times as many erasers as Leona. Leona has 8 erasers. How many erasers does Gabriella have?
Options:
a. 32
b. 24
c. 12
d. 2

a. 32

Explanation:
Gabriella has 4 x 8 = 32 erasers.

Question 6.
Phil has 3 times as many rocks as Peter. Together, they have 48 rocks. How many more rocks does Phil have than Peter?
Options:
a. 36
b. 24
c. 16
d. 12

b. 24

Explanation:
Phil has 3 times as many rocks as Peter. Together, they have 48 rocks
If Peter has x rocks, Phil has 3x rocks
3x + x = 48.
4x = 48.
x = 48/4 = 12.
Peter has 12 rocks. Phil has 3 x 12 = 36 rocks.
Phil has 36 – 12 = 24 more rocks than Peter.

### Page No. 179

Question 1.
Find the product.

Estimate: ______
Product: _______

Estimate: 1,500
Product: 1,566

Explanation:
54 x 29
Estimate: Think 54 is close to 50; 29 is close to 30.
50 x 30 = 1,500
Product:
20 x 5 tens = 100 tens
20 x 4 ones = 80 ones
9 x 5 tens = 45 tens
9 x 4 ones = 36 ones.
1000 + 80 + 450 + 36 = 1,566.

Estimate. Then choose a method to find the product.

Question 3.
6 3
× 4 2
——-
Estimate: ______
Product: _______

Estimate: 2,400
Product: 2646

Explanation:
63 x 42
Estimate: Think 63 is close to 60; 42 is close to 40.
60 x 40 = 2400
Product:
40 x 6 tens = 240 tens
40 x 3 ones = 120 ones
2 x 6 tens = 12 tens
2 x 3 ones = 6 ones.
2400 + 120 + 120 + 6 = 2646.

Question 4.
8 4
× 5 3
——-
Estimate: ______
Product: _______

Estimate: 4,000
Product: 4,452

Explanation:
84 x 53
Estimate: Think 84 is close to 80; 53 is close to 50.
80 x 50 = 4,000
Product:
50 x 8 tens = 400 tens
50 x 4 ones = 200 ones
3 x 8 tens = 24 tens
3 x 4 ones = 12 ones.
4000 + 200 + 240 + 12 = 4,452.

Question 5.
7 1
× 1 3
——-
Estimate: ______
Product: _______

Estimate: 700
Product: 923

Explanation:
71 x 13
Estimate: Think 71 is close to 70; 13 is close to 10.
70 x 10 = 700
Product:
10 x 7 tens = 70 tens
10 x 1 ones = 10 ones
3 x 7 tens = 21 tens
3 x 1 ones = 3 ones.
700 + 10 + 210 + 3 = 923.

Practice: Copy and Solve Estimate. Find the product.

Question 6.
29 × $82 Estimate:$ _______
Product: $_______ Answer: Estimate:$2,400
Product: $2,378 Explanation: 29 x$82
Estimate: Think 29 is close to 30; $82 is close to$80.
30 x $80 =$2,400
Product:
$80 x 2 tens =$160 tens
$80 x 9 ones =$720 ones
$2 x 2 tens =$4 tens
$2 x 9 ones =$18 ones.
$1600 +$720 + $40 +$18 = $2,378. Question 7. 57 × 79 Estimate: _______ Product: _______ Answer: Estimate: 4,800 Product: 4,503 Explanation: 57 x 79 Estimate: Think 57 is close to 60; 79 is close to 80. 60 x 80 = 4,800 Product: 70 x 5 tens = 350 tens 70 x 7 ones = 490 ones 9 x 5 tens = 45 tens 9 x 7 ones = 63 ones. Add partial products. 3500 + 490 + 450 + 63 = 4,503. Question 8. 80 × 27 Estimate: _______ Product: _______ Answer: Estimate: 2,400 Product: 2,160 Explanation: 80 x 27 Estimate: Think 27 is close to 30. 30 x 80 = 2,400 Product: 20 x 8 tens = 160 tens 20 x 0 ones = 0 ones 7 x 8 tens = 56 tens 7 x 0 ones = 0 ones. Add partial products. 1600 + 0 + 560 + 0 = 2,160. Question 9. 32 ×$75
Estimate: $_______ Product:$ _______

Estimate: $2,100 Product:$2,400

Explanation:
32 × $75 Estimate: Think 32 is close to 30;$75 is close to $70. 30 x$70 = $2,100 Product:$70 x 3 tens = $210 tens$70 x 2 ones = $140 ones$5 x 3 tens = $15 tens$5 x 2 ones = $10 ones. Add partial products.$2100 + $140 +$150 + $10 =$2,400.

Question 10.
55 × 48
Estimate: _______
Product: _______

Estimate: 2,750
Product: 2,640

Explanation:
55 × 48
Estimate: Think 48 is close to 50.
55 x 50 = 2,750
Product:
40 x 5 tens = 200 tens
40 x 5 ones = 200 ones
8 x 5 tens = 40 tens
8 x 5 ones = 40 ones.
2000 + 200 + 400 + 40 = 2,640.

Question 11.
19 × $82 Estimate:$ _______
Product: $_______ Answer: Estimate:$1,600
Product: $1,558 Explanation: 19 ×$82
Estimate: Think 19 is close to 20; $82 is close to$80.
20 x $80 =$1,600
Product:
$80 x 1 tens =$80 tens
$80 x 9 ones =$720 ones
$2 x 1 tens =$2 tens
$2 x 9 ones =$18 ones.
$800 +$720 + $20 +$18 = $1,558. Question 12. 25 ×$25
Estimate: $_______ Product:$ _______

Estimate: $625 Product:$625

Explanation:
25 × $25 Estimate: 25 x$25 = $625 Product:$20 x 2 tens = $40 tens$20 x 5 ones = $100 ones$5 x 2 tens = $10 tens$5 x 5 ones = $25 ones. Add partial products.$400 + $100 +$100 + $25 =$625.

Question 13.
41 × 98
Estimate: _______
Product: _______

Estimate: 4,000
Product: 4,018

Explanation:
41 × 98
Estimate: Think 41 is close to 40; 98 is close to 100.
40 x 100 = 4,000
Product:
90 x 4 tens = 360 tens
90 x 1 ones = 90 ones
8 x 4 tens = 32 tens
8 x 1 ones = 8 ones.
3600 + 90 + 320 + 8 = 4,018.

Identify Relationships Algebra Use mental math to find the number.

### Page No. 180

Question 18.
Martin collects stamps. He counted 48 pages in his collector’s album. The first 20 pages each have 35 stamps in 5 rows. The rest of the pages each have 54 stamps. How many stamps does Martin have in his album?

a. What do you need to know?
Type below:
_________

The total stamps in the first 20 pages + The total stamps in the remaining pages.

Question 18.
b. How will you use multiplication to find the number of stamps?
Type below:
_________

The first 20 pages each have 35 stamps in 5 rows.
So, 35 x 5 = 175 stamps.

Question 18.
c. Tell why you might use addition and subtraction to help solve the problem.
Type below:
_________

As mentioned that the number of stamps available in the first 20 pages and the number of stamps available in the rest of the pages. We need to add all pages to get 48 pages stamps.

Question 18.
d. Show the steps to solve the problem.
Type below:
_________

Martin has 48 pages in his collector’s album.
The first 20 pages each have 35 stamps in 5 rows.
So, 35 x 5 = 175 stamps.
The first 20 pages have 175 stamps.
The rest of the pages each have 54 stamps.
So, total stamps = 175 + 54 = 229 stamps.

Question 18.
e. Complete the sentences.
Martin has a total of _____ stamps on the first 20 pages.
There are _____ more pages after the first 20 pages in Martin’s album.
There are _____ stamps on the rest of the pages.
There are _____ stamps in the album.
Type below:
_________

Martin has a total of __175___ stamps on the first 20 pages.
There are __24___ more pages after the first 20 pages in Martin’s album.
There are __54___ stamps on the rest of the pages.
There are ___229__ stamps in the album.

Question 19.
Select the expressions that have the same product as 35 × 17. Mark all that apply.
Options:
a. (30 × 10) + (30 × 7) + (5 × 10) + (5 × 7)
b. (30 × 17) + (5 × 17)
c. (35 × 30) + (35 × 5) + (35 × 10) + (35 × 7)
d. (35 × 10) + (35 × 7)
e. (35 × 10) + (30 × 10) + (5 × 10) + (5 × 7)
f. (35 × 30) + (35 × 5)

a. (30 × 10) + (30 × 7) + (5 × 10) + (5 × 7)
b. (30 × 17) + (5 × 17)
d. (35 × 10) + (35 × 7)

Explanation:
35 × 17
30 x 10 =300
30 x 7 = 210
5 x 10 = 50
5 x 7 = 35
300 + 210 + 50 + 35 = 595.
a. (30 × 10) + (30 × 7) + (5 × 10) + (5 × 7) = 300 + 210 + 50 + 35 = 595 equal to 595.
b. (30 × 17) + (5 × 17) = 510 + 85 = 595 equal to 595.
c. (35 × 30) + (35 × 5) + (35 × 10) + (35 × 7) = 1050 + 175 + 350 + 245 = 1820 not equal to 595.
d. (35 × 10) + (35 × 7) = 350 + 245 = 595 equal to 595
e. (35 × 10) + (30 × 10) + (5 × 10) + (5 × 7) = 350 + 300 + 50 + 35 = 735 not equal to 595.
f. (35 × 30) + (35 × 5) = 1050 + 175 = 1,225 not equal to 595.

### Common Core – Page No. 181

Choose a Multiplication Method

Estimate. Then choose a method to find the product.

Question 1.
Estimate: 1,200
3 1
× 4 3
——-
9 3
+ 1, 2 4 0
————
1, 3 3 3

Estimate: 1,200
Product: 1, 3 3 3

Explanation:
Estimate: 1,200
3 1
× 4 3
——-
9 3
+ 1, 2 4 0
————
1, 3 3 3

Question 2.
6 7
× 8 5
——-
Estimate: _____
Product: ______

Estimate: 6,300
Product: 5,695

Explanation:
Estimate: 67 is close to 70; 85 is close to 90.
70 x 90 = 6,300.
Product: 67 x 85
80 x 6 tens = 480 tens
80 x 7 ones = 560 ones
5 x 6 tens = 30 tens
5 x 7 ones = 35 ones.
4800 + 560 + 300 + 35 = 5,695.

Question 3.
6 8
× 3 8
——-
Estimate: _____
Product: ______

Estimate: 2,800
Product: 2,584

Explanation:
Estimate: 68 is close to 70; 38 is close to 40.
70 x 40 = 2,800.
Product: 68 x 38
30 x 6 tens = 180 tens
30 x 8 ones = 240 ones
8 x 6 tens = 48 tens
8 x 8 ones = 64 ones.
1800 + 240 + 480 + 64 = 2,584.

Question 4.
9 5
× 1 7
——-
Estimate: _____
Product: ______

Estimate: 1,700
Product: 1,615

Explanation:
Estimate: 95 is close to 100.
100 x 17 = 1,700.
Product: 95 x 17
10 x 9 tens = 90 tens
10 x 5 ones = 50 ones
7 x 9 tens = 63 tens
7 x 5 ones = 35 ones.
900 + 50 + 630 + 35 = 1,615.

Question 5.
4 9
× 5 4
——-
Estimate: _____
Product: ______

Estimate: 2,500
Product: 2,646

Explanation:
Estimate: 49 is close to 50; 54 is close to 50.
50 x 50 = 2,500.
Product: 49 x 54
50 x 4 tens = 200 tens
50 x 9 ones = 450 ones
4 x 4 tens = 16 tens
4 x 9 ones = 36 ones.
2000 + 450 + 160 + 36 = 2,646.

Question 6.
9 1
× 2 6
——-
Estimate: _____
Product: ______

Estimate: 2,700
Product: 2,366

Explanation:
Estimate: 91 is close to 90; 26 is close to 30.
90 x 30 = 2,700.
Product: 49 x 54
20 x 9 tens = 180 tens
20 x 1 ones = 20 ones
6 x 9 tens = 54 tens
6 x 1 ones = 6 ones.
1800 + 20 + 540 + 6 = 2,366.

Question 7.
8 2
× 1 9
——-
Estimate: _____
Product: ______

Estimate: 1,600
Product: 1,558

Explanation:
Estimate: 82 is close to 80; 19 is close to 20.
80 x 20 = 1,600.
Product: 82 x 19
10 x 8 tens = 80 tens
10 x 2 ones = 20 ones
9 x 8 tens = 72 tens
9 x 2 ones = 18 ones.
800 + 20 + 720 + 18 = 1,558.

Question 8.
4 6
× 2 7
——-
Estimate: _____
Product: ______

Estimate: 1,500
Product: 1,242

Explanation:
Estimate: 46 is close to 50; 27 is close to 30.
50 x 30 = 1,500.
Product: 46 x 27
20 x 4 tens = 80 tens
20 x 6 ones = 120 ones
7 x 4 tens = 28 tens
7 x 6 ones = 42 ones.
800 + 120 + 280 + 42 = 1,242.

Question 9.
4 1
× 3 3
——-
Estimate: _____
Product: ______

Estimate: 1,200
Product: 1,353

Explanation:
Estimate: 41 is close to 40; 33 is close to 30.
40 x 30 = 1,200.
Product: 41 x 33
30 x 4 tens = 120 tens
30 x 1 ones = 30 ones
3 x 4 tens = 12 tens
3 x 1 ones = 3 ones.
1200 + 30 + 120 + 3 = 1,353.

Question 10.
9 7
× 1 3
——-
Estimate: _____
Product: ______

Estimate: 1,300
Product: 1,261

Explanation:
Estimate: 97 is close to 100.
100 x 13 = 1,300.
Product: 97 x 13
10 x 9 tens = 90 tens
10 x 7 ones = 70 ones
3 x 9 tens = 27 tens
3 x 7 ones = 21 ones.
900 + 70 + 270 + 21 = 1,261.

Question 11.
7 5
× 6 9
——-
Estimate: _____
Product: ______

Estimate: 5,600
Product: 5,195

Explanation:
Estimate: 75 is close to 80; 69 is close to 70.
80 x 70 = 5,600.
Product: 75 x 69
60 x 7 tens = 420 tens
60 x 5 ones = 300 ones
9 x 7 tens = 63 tens
9 x 5 ones = 45 ones.
4200 + 300 + 630 + 45 = 5,195.

Problem Solving

### Common Core – Page No. 182

Lesson Check

Question 1.
A choir needs new robes for each of its 46 singers. Each robe costs $32. What will be the total cost for all 46 robes? Options: a.$1,472
b. $1,372 c.$1,362
d. $230 Answer: a.$1,472

Explanation:
46 x $32 40 x$32 = $1,280 6 x$32 = $192$1,280 + $192 =$1,472

Question 2.
A wall on the side of a building is made up of 52 rows of bricks with 44 bricks in each row. How many bricks make up the wall?
Options:
a. 3,080
b. 2,288
c. 488
d. 416

b. 2,288

Explanation:
52 x 44
50 x 44 = 2,200
2 x 44 = 88
2,200 + 88 = 2,288.
2,288 bricks make up the wall.

Spiral Review

Question 3.
Which expression shows how to multiply 4 × 362 by using place value and expanded form?
Options:
a. (4 × 3) + (4 × 6) + (4 × 2)
b. (4 × 300) + (4 × 600) +(4 × 200)
c. (4 × 300) + (4 × 60) + (4 × 20)
d. (4 × 300) + (4 × 60) + (4 × 2)

d. (4 × 300) + (4 × 60) + (4 × 2)

Explanation:
4 × 362 = 1,448
a. (4 × 3) + (4 × 6) + (4 × 2) = 12 + 24 + 8 = 44 not equal to 1,448.
b. (4 × 300) + (4 × 600) +(4 × 200) = 1200 + 2400 + 800 = 4,400 not equal to 1,448.
c. (4 × 300) + (4 × 60) + (4 × 20) = 1200 + 240 + 80 = 1,520 not equal to 1,448.
d. (4 × 300) + (4 × 60) + (4 × 2) = 1200 + 240 + 8 = 1,448 equal to 1,448.

Question 4.
Use the model below. What is the product 4 x 492?

Options:
a. 16 + 36 + 8 = 60
b. 160 + 36 + 8 = 204
c. 160 + 360 + 8 = 528
d. 1,600 + 360 + 8 = 1,968

d. 1,600 + 360 + 8 = 1,968

Explanation:

1,600 + 360 + 8 = 1,968

Question 5.
What is the sum 13,094 + 259,728?
Options:
a. 272,832
b. 272,822
c. 262,722
d. 262,712

c. 262,722

Explanation:
13,094 + 259,728 = 262,722

Question 6.
During the 2008–2009 season, there were 801,372 people who attended the home hockey games in Philadelphia. There were 609,907 people who attended the home hockey games in Phoenix. How much greater was the home attendance in Philadelphia than in Phoenix that season?
Options:
a. 101,475
b. 191,465
c. 201,465
d. 202,465

b. 191,465

Explanation:
801,372 – 609,907 = 191,465
Philadelphia attendance is 191,465 greater than in Phoenix that season.

### Page No. 185

Question 1.
An average of 74 reports with bird counts were turned in each day in June. An average of 89 were turned in each day in July. How many reports were turned in for both months? (Hint: There are 30 days in June and 31 days in July.)
First, write the problem for June.
Type below:
__________

Given that An average of 74 reports with bird counts was turned in each day in June.
For June Month, there are 30 days = 30 x 74 = 2,220.

Question 1.
Next, write the problem for July.
Type below:
__________

An average of 89 reports with bird counts was turned in each day in July.
For July Month, there are 31 days = 31 x 89 = 2,759.

Question 1.
Last, find and add the two products.
____________ reports were turned in for both months.
Type below:
__________

Given that An average of 74 reports with bird counts was turned in each day in June.
For June Month, there are 30 days = 30 x 74 = 2,220.
An average of 89 reports with bird counts was turned in each day in July.
For July Month, there are 31 days = 31 x 89 = 2,759.
Add two products to get the total number of reports that were turned in for both months.
2,220 + 2,759 = 4,979.

Question 2.
What if an average of 98 reports were turned in each day for the month of June? How many reports were turned in for June? Describe how your answer for June would be different.
______ reports

720 more reports

Explanation:
Given that an average of 98 reports was turned in each day for the month of June.
June has 30 days.
Total number of reports were turned in for June = 30 x 98 = 2, 940.
From the above answer, 98 − 74 = 24. So, there would be 30 × 24, or 720 more reports.

Question 3.
There are 48 crayons in a box. There are 12 boxes in a carton. Mr. Johnson ordered 6 cartons of crayons for the school. How many crayons did he get?
______ crayons

3,456 crayons

Explanation:
There are 48 crayons in a box.
There are 12 boxes in a carton.
So, 1 carton = 48 x 12 = 576 crayons.
If Mr. Johnson ordered 6 cartons of crayons for the school, 6 x 576 crayons = 3,456 crayons.
He gets 3,456 crayons.

Question 4.
Make Sense of Problems Each of 5 birdwatchers reported seeing 15 roseate spoonbills in a day. If they each reported seeing the same number of roseate spoonbills over 14 days, how many would be reported?
______ roseate spoonbills

1,050 roseate spoonbills

Explanation:
Given that, 1 day –>5 birdwatchers reported 15 roseate spoonbills = 5 x 15 = 75 roseate spoonbills.
So, in 14 days –> 5 birdwatchers reported 75 x 14 = 1,050 roseate spoonbills.

### Page No. 186

Question 7.
Lydia is having a party on Saturday. She decides to write a riddle on her invitations to describe her house number on Cypress Street. Use the clues to find Lydia’s address.

______ Cypress Street

14827 Cypress Street

Explanation:
Given that tens digit is 5 less than 7 = 7 – 5 = 2. 2 is the tens digit.
The thousands digit is twice the digit in the tens place = 2 x 2 = 4.
The hundreds digit is the greatest even number that is less than 10 i.e, 8.
The ones digit is the product of 7 and 1 = 7 x 1 = 7.
The ten thousands digit is the difference between the hundreds digit and the ones digit. So, 8 – 7 = 1.
Lydia’s address ( house number ) is 14827 Cypress Street.

Question 8.
A school is adding 4 rows of seats to the auditorium. There are 7 seats in each row. Each new seat costs $99. What is the total cost for the new seats? Show your work.$ ______

$2,772 Explanation: Given that A school is adding 4 rows of seats to the auditorium. There are 7 seats in each row. So, 7 x 4 = 28 seats are available in an auditorium. Each new seat costs$99.
28 x $99 =$2,772 for total cost of the new seats.

### Common Core – Page No. 187

Problem Solving Multiply 2 – Digit numbers

Solve each problem. Use a bar model to help.

Question 1.
Mason counted an average of 18 birds at his bird feeder each day for 20 days. Gloria counted an average of 21 birds at her bird feeder each day for 16 days. How many more birds did Mason count at his feeder than Gloria counted at hers?

Birds counted by Mason: 18 × 20 = 360
Birds counted by Gloria: 21 × 16 = 336
Draw a bar model to compare.
Subtract. 360 – 336 = 24
So, Mason counted 24 more birds.

Birds counted by Mason: 18 × 20 = 360
Birds counted by Gloria: 21 × 16 = 336
Draw a bar model to compare.

Subtract. 360 – 336 = 24
So, Mason counted 24 more birds.

Question 2.
The 24 students in Ms. Lee’s class each collected an average of 18 cans for recycling. The 21 students in Mr. Galvez’s class each collected an average of 25 cans for recycling. How many more cans were collected by Mr. Galvez’s class than Ms. Lee’s class?
______ more cans

The number of cans collected by Ms. Lee’s class = 18 x 24 = 432.
The number of cans collected by Mr. Galvez’s class = 25 x 21 = 525.
Use Bar Model

Subtract. 525 – 432 = 93 more cans.
So, Mr. Galvez’s class collected 93 more cans than Ms. Lee’s class.

Question 3.
At East School, each of the 45 classrooms has an average of 22 students. At West School, each of the 42 classrooms has an average of 23 students. How many more students are at East School than at West School?
______ more students

Students in East school = 45 x 22 = 990.
Students in West School = 42 x 23 = 966.
Use Bar Model

Subtract. 990 – 966 = 24.
So, East School has 24 students more than West School.

Question 4.
A zoo gift shop orders 18 boxes of 75 key rings each and 15 boxes of 80 refrigerator magnets each. How many more key rings than refrigerator magnets does the gift shop order?
______ more key rings

Number of Key Rings = 75 x 18 = 1,350.
Number of Refrigerator Magnets= 80 x 15 = 1,200.
Use Bar Model

Subtract. 1,350 – 1,200 = 150.
So, key rings are 150 more than refrigerator magnets.

### Common Core – Page No. 188

Lesson Check

Question 1.
Ace Manufacturing ordered 17 boxes with 85 ball bearings each. They also ordered 15 boxes with 90 springs each. How many more ball bearings than springs did they order?
Options:
a. 5
b. 85
c. 90
d. 95

d. 95

Explanation:
Number of ball bearings = 85 x 17 = 1,445.
Number of springs = 90 x 15 = 1,350.
Use Bar Model

Subtract. 1,445 – 1,350 = 95.
So, ball bearings are 95 more than springs.

Question 2.
Elton hiked 16 miles each day on a 12-day hiking trip. Lola hiked 14 miles each day on her 16-day hiking trip. In all, how many more miles did Lola hike than Elton hiked?
Options:
a. 2 miles
b. 18 miles
c. 32 miles
d. 118 miles

c. 32 miles

Explanation:
Hiking trip by Elton = 12 x 16 = 192.
Hiking trip by Lola = 16 x 14 = 224.
Use Bar Model

Subtract. 224 – 192 = 32.
So, the Hiking trip by Lola is 32 times more than the Hiking trip by Elton.

Spiral Review

Question 3.
An orchard has 24 rows of apple trees. There are 35 apple trees in each row. How many apple trees are in the orchard?
Options:
a. 59
b. 192
c. 740
d. 840

d. 840

Explanation:
An orchard has 24 rows of apple trees. There are 35 apple trees in each row.
24 x 35 = 840 apple trees are in the orchard.

Question 4.
An amusement park reported 354,605 visitors last summer. What is this number rounded to the nearest thousand?
Options:
a. 354,600
b. 355,000
c. 360,000
d. 400,000

b. 355,000

Explanation:
An amusement park reported 354,605 visitors last summer. 4,605 is close to 5,000. So, the answer is 355,000.

Question 5.
Attendance at the football game was 102,653. What is the value of the digit 6?
Options:
a. 6
b. 60
c. 600
d. 6,000

c. 600

Explanation:
Digit 6 is at hundreds of positions. So, the answer is 6 x 100 = 600.

Question 6.
Jill’s fish weighs 8 times as much as her parakeet. Together, the pets weigh 63 ounces. How much does the fish weigh?
Options:
a. 7 ounces
b. 49 ounces
c. 55 ounces
d. 56 ounces

d. 56 ounces

Explanation:
Let Jill’s parakeet = X.
Jill’s fish weighs 8 times as much as her parakeet = 8X.
Together, the pets weigh 63 ounces.
X + 8X = 63.
9X = 63.
X = 63/9 = 7.
So, Jill’s parakeet =7.
Jill’s fish = 7 x 8 = 56 ounces.

### Review/Test – Page No. 189

Mrs. Traynor’s class is taking a field trip to the zoo. The trip will cost $26 for each student. There are 22 students in her class. Question 2. Part A Round each factor to estimate the total cost of the student’s field trip.$ ______

$600 Explanation: Total cost of the students’ field trip = 22 x$26.
22 x $26 20 x$30 = $600 The total cost would be about$600.

Question 2.
Part B
Use compatible numbers to estimate the total cost of the field trip.
$______ Answer:$500

Explanation:
If we use compatible numbers to estimate the total cost of the field trip.
22 x $26 20 × 25 = 500 The total cost would be about$500.

Question 2.
Part C
Which do you think is the better estimate? Explain.
Better estimate: _________

Using rounded numbers is a better estimate. When rounded numbers are used, one estimated factor was $4 more than the actual factor and the other estimated factor was$2 that is less than the actual factor. So, the estimate should be close to the actual one. When compatible numbers are used both estimated factors were less than the actual factors. So, the product will be an underestimate.

### Review/Test – Page No. 190

For numbers 3a–3e, select Yes or No to show if the answer is correct.

Question 3.
3a. 35 × 10 = 350
i. yes
ii. no

i. yes

Explanation:
35 x 10 = 350
30 x 10 = 300.
5 x 10 = 50.
300 + 50 = 350.

Question 3.
3b. 19 × 20 = 380
i. yes
ii. no

i. yes

Explanation:
19 × 20 = 380
19 x 20 = 19 x 2 tens.
19 x 20 = 38 tens = 380.

Question 3.
3c. 12 × 100 = 120
i. yes
ii. no

ii. no

Explanation:
12 x 100 = 120.
10 x 100 = 1000
2 x 100 = 200.
1000 + 200 = 1200.

Question 3.
3d. 70 × 100 = 7,000
i. yes
ii. no

i. yes

Explanation:
70 x 100 = 7,000
100 x 7 tens = 700 tens = 7,000

Question 3.
3e. 28 × 30 = 2,100
i. yes
ii. no

ii. no

Explanation:
28 × 30
20 x 30 = 600
8 x 30 = 240
600 + 240 = 840

Question 5.
Which would provide a reasonable estimate for each product? Write the estimate beside the product. An estimate may be used more than once
23 × 38 __________
31 × 32 __________
46 × 18 __________
39 × 21 __________

23 × 38 –> 25 x 40
31 x 32 –> 30 × 30
46 × 18 –> 50 × 20
39 × 21 –> 25 × 40

Explanation:
23 × 38; 23 is close to 25; 38 is close to 40.
So, the estimated product is 25 x 40
31 x 32; 31 is close to 30; 32is close to 30.
So, the estimated product is 30 × 30
46 × 18; 46 is close to 50; 18 is close to 20.
So, the estimated product is 50 × 20
39 × 21; 39 is close to 40; 21 is close to 25.
So, the estimated product is 25 × 40

Question 6.
There are 26 baseball teams in the league. Each team has 18 players. Write a number sentence that will provide a reasonable estimate for the number of players in the league. Explain how you found your estimate.
Type below:
__________

There are 26 baseball teams in the league. Each team has 18 players.
26 x 18
25 x 20
We Rounded each factor to its close factor, then simplified the multiplication.

Question 7.
The model shows 48 × 37. Write the partial products.

Type below:
__________

Partial Products are 1200, 240, 280, 56

### Review/Test – Page No. 191

Question 8.
Jess made this model find the product 32 × 17. Her model is incorrect.

Part A
What did Jess do wrong?
Type below:
__________

Question 8.
Part B
Redraw the model so that it is correct.

Type below:
__________

Question 8.
Part C
What is the actual product 32 × 17?
______

544

Explanation:
32 × 17
10 x 32 = 320
7 x 32 = 224
320 + 224 = 544.

Question 9.
Tatum wants to use partial products to find 15 × 32. Write the numbers in the boxes to show 15 × 32.

Type below:
__________

### Review/Test – Page No. 192

Question 10.
Which product is shown by the model? Write the letter of the product on the line below the model.

Type below:
__________

C                                              A                                                  B
10 + 3 = 13
10 + 3 = 13
13 x 13
2. 10 + 7 = 17
30 + 6 = 36
17 x 36
3. 20 + 4 = 24
10 + 4 = 14
24 x 14

Question 12.
Write the unknown digits. Use each digit exactly once.

Type below:
__________

90 x 40 = 3,600
90 x 6 = 540
3 x 40 = 120
3 x 6 = 18.
3,600 + 540 + 120 + 8 = 4,278.

Question 13.
Mike has 16 baseball cards. Niko has 17 times as many baseball cards as Mike does. How many baseball cards does Niko have?
________ baseball cards

272 baseball cards

Explanation:
Mike has 16 baseball cards. Niko has 17 times as many baseball cards as Mike does.
Niko have 16 x 17 = 272 baseball cards.

Question 14.
Multiply.
36 × 28 = ________

1,008

Explanation:
36 x 28
20 x 30 = 600
20 x 6 = 120
8 x 30 = 240
8 x 6 = 48
600 + 120 + 240 + 48 = 1,008

### Review/Test – Page No. 193

Question 16.
Select another way to show 25 × 18. Mark all that apply.
Options:
a. (20 × 10) + (20 × 8) + (5 × 10) + (5 × 8)
b. (25 × 20) + (25 × 5) + (25 × 10) + (25 × 8)
c. (20 × 18) + (5 × 10) + (5 × 8)
d. (25 × 10) + (25 × 8)
e. (25 × 20) + (25 × 5)

a. (20 × 10) + (20 × 8) + (5 × 10) + (5 × 8)
c. (20 × 18) + (5 × 10) + (5 × 8)
d. (25 × 10) + (25 × 8)

Explanation:
25 × 18
10 x 25 = 250
8 x 25 = 200
250 + 200 = 450.
a. (20 × 10) + (20 × 8) + (5 × 10) + (5 × 8) = 200 + 160 + 50 + 40 = 450
b. (25 × 20) + (25 × 5) + (25 × 10) + (25 × 8) = 500 + 125 + 250 + 200 = 1,075
c. (20 × 18) + (5 × 10) + (5 × 8) = 360 + 50 + 40 = 450
d. (25 × 10) + (25 × 8) = 250 + 200 = 450
e. (25 × 20) + (25 × 5) = 500 + 125 = 625

Question 17.
Terrell runs 15 sprints. Each sprint is 65 meters. How many meters does Terrell run? Show your work.
______ meters

975 meters

Explanation:
Terrell run 15 x 65 = 975 meters.

Question 18.
There are 3 new seats in each row in a school auditorium. There are 15 rows in the auditorium. Each new seat cost $74. What is the cost for the new seats? Explain how you found your answer.$ ______

$3,330 Explanation: Given that There are 3 new seats in each row in a school auditorium. There are 15 rows in the auditorium. Each new seat cost$74.
So, 3 x 15 = 45 seats are available in an auditorium.
Each new seat costs $74. 45 x$74 = $3,330 for total cost of the new seats. Question 19. Ray and Ella helped move their school library to a new building. Ray packed 27 boxes with 25 books in each box. Ella packed 23 boxes with 30 books in each box. How many more books did Ella pack? Show your work. ______ books Answer: 15 books Explanation: Ray packed 27 x 25 = 675 books. Ella packed 23 x 30 = 690 books Ella packed 690 – 675 = 15 books more than Ray. ### Review/Test – Page No. 194 Question 20. Julius and Walt are finding the product of 25 and 16. Part A Julius’ answer is incorrect. What did Julius do wrong? Type below: __________ Answer: Julius multiplied 25 by 10 and then multiplied 25 by 6 correctly. He added the two partial products incorrectly. Question 20. Part B What did Walt do wrong? Type below: __________ Answer: Walt multiplied 6 by 5 and got 300 instead of 30 Question 20. Part C What is the correct product? Type below: __________ Answer: 25 x 16 = 400 Question 21. A clothing store sells 26 shirts and 22 pairs of jeans. Each item of clothing costs$32.
Part A
What is a reasonable estimate for the total cost of the clothing?
$______ Answer:$1500

Explanation:
A clothing store sells 26 shirts and 22 pairs of jeans. 26 + 22 = 48 clothes.
Each item of clothing costs $32. 48 x$32
50 x $30 =$1500

Question 21.
Part B
What is the exact answer for the total cost of the clothing? Show or explain how you found your answer.
$______ Answer:$1,536

Explanation:
48 x $32 40 x$32 = $1,280 8 x$32 = $256$1,280 + $256 =$1,536

### Page No. 199

Question 1.
A restaurant has 68 chairs. There are six chairs at each table. About how many tables are in the restaurant?
Estimate. 68 ÷ 6
Think: What number times 6 is about 68?
10 × 6 = ___
11 × 6 = ___
12 × 6 = ___
68 is closest to ______, so the best estimate is about _______ tables are in the restaurant.
Type below:
__________

68 is close to 70 and 6 is close to 5.
So, 70/5 = 12.
10 × 6 = __60_
11 × 6 = _66__
12 × 6 = _72__
68 is closest to ___66___, so the best estimate is about 11 x 6 = 66 tables are in the restaurant.

Find two numbers the quotient is between. Then estimate the quotient.

Find two numbers the quotient is between. Then estimate the quotient.

Question 4.
90 ÷ 7
between _______ and _______

between 12 and 13

Explanation:
12 x 7 = 84; 13 x 7 = 91.
The quotient of 90 ÷ 7 is between 12 and 13.

Question 5.
67 ÷ 4
between _______ and _______

between 16 and 17

Explanation:
16 x 4 = 64; 17 x 4 = 68.
The quotient of 67 ÷ 4 is between 16 and 17.

Question 6.
281 ÷ 9
between _______ and _______

between 30 and 40

Explanation:
30 x 9 = 270; 40 x 9 = 360.
The quotient of 281 ÷ 9 is between 30 and 40.

Question 7.
102 ÷ 7
between _______ and _______

between 14 and 15

Explanation:
14 x 7 = 98; 15 x 7 = 105.
The quotient of 102 ÷ 7 is between 14 and 15.

Question 8.
85 ÷ 6
between _______ and _______

between 14 and 15

Explanation:
14 x 6 = 84; 15 x 6 = 90.
The quotient of 85 ÷ 6 is between 14 and 15.

Question 9.
220 ÷ 8
between _______ and _______

between 20 and 30

Explanation:
20 x 8 = 160; 30 x 8 = 240.
The quotient of 220 ÷ 8 is between 20 and 30.

Decide whether the actual quotient is greater than or less than the estimate given. Write < or >.

Question 10.
83 ÷ 8 _______ 10

>

Explanation:
83 ÷ 8 = 10.375 > 10

Question 11.
155 ÷ 4 _______ 40

<

Explanation:
155 ÷ 4 = 38.75 < 40

Question 12.
70 ÷ 6 _______ 11

>

Explanation:
70 ÷ 6 = 11.666 > 11

Question 13.
What’s the Question? A dolphin’s heart beats 688 times in 6 minutes. Answer: about 100 times.
Type below:
__________

About how many times does a dolphin’s heart beats in 1 minute?

Question 14.
Analyze A mother bottlenose ate about 278 pounds of food in one week. About how much food did she eat in a day?

Explanation:
278 ÷ 7
The quotient of 278 ÷ 7 is between 39 and 40.

### Page No. 200

Question 16.
If a bottlenose dolphin can eat 175 pounds of fish, squid, and shrimp in a week, how many pounds of food does it eat in a day? Milo says the answer is about 20 pounds. Leah says the answer is about 30 pounds. Who is correct? Explain.

________

The bottlenose dolphin can eat 25 pounds in 1 day.
Both answers are correct. Because 25 pounds is between 20 and 30 pounds.

Explanation:
1 week = 7 days.
The bottlenose dolphin can eat 175 pounds for 7 days.
For 1 day = 175 ÷ 7 = 25 pounds.
The bottlenose dolphin can eat 25 pounds in 1 day.
Both answers are correct. Because 25 pounds is between 20 and 30 pounds.

Question 17.
Four families went out for lunch. The total food bill came to $167. The families also left a$30 tip for the waitress. If each family spent the same amount, how much did each family spend on dinner? Explain how you found your answer.
$______ Answer:$98.5

Explanation:
Four families went out for lunch. The total food bill came to $167. The families also left a$30 tip for the waitress.
So, total amount = $167 +$30 = $197. If each family spent the same amount =$197 ÷ 2 = $98.5 Each family spent$98.5.

Question 18.
There are 6 showings of a film about Van Gogh at the Art Museum. A total of 459 people saw the film. The exact number of people were at each show. About how many people were at each show? Circle the numbers the quotient is between. Then explain how you found your answer.
40 50 60 70 80
Type below:
_________

40 50 60 70 80
I found multiples of 6 that 459 is between. 70 × 6 = 420 and 80 × 6 = 480. Since 459 is closer to 480, 459 ÷ 6 is about 80.

### Conclusion

Hope the data shared about Go Math Grade 4 Answer Key Chapter 3 Multiply 2- Digit Number has helped you in your preparation. If you feel any learning is missing do give us your suggestions and we will consider them if possible. Just keep on visiting our site to get the latest update on Grade 4 Go Math HMH Answer Keys for other chapters as well.

## Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Go Math Solutions Resource is the best guide for students of 4th grade. In Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers you will find the questions and their detailed solutions in an easy manner. By using the 4th Standard Go Math solutions key everyone can prepare all chapter 2 topics easily & score well in the exams. This Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers will let students grasp the concepts properly & make them practice more regularly.

## Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Practicing each and every step by step explained questions will provide immense results. Students can easily understand the topics of chapter 2 Multiply by 1-Digit Numbers via Go Math 4th Grade Answer Key. You will look up the concepts called Multiplication Comparisons, Multiplying using Distributive property and Expanded form, Estimate products, etc. clearly through this Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers for standard knowledge of the subject.

Lesson 1: Algebra • Multiplication Comparisons

Lesson 2: Algebra • Comparison Problems

Lesson 3: Multiply Tens, Hundreds, and Thousands

Lesson 4: Estimate Products

Lesson 5: Investigate • Multiply Using the Distributive Property

Lesson 6: Multiply Using Expanded Form

Lesson 7: Multiply Using Partial Products

Lesson 8: Multiply Using Mental Math

Lesson 9: Problem Solving • Multistep Multiplication Problems

Lesson 10: Multiply 2-Digit Numbers with Regrouping

Lesson 11: Multiply 3-Digit and 4-Digit Numbers with Regrouping

Lesson 12: Algebra • Solve Multistep Problems Using Equations

Chapter 2 Review/Test

### Common Core – Multiplication Comparisons – Page No. 67

Write a comparison sentence.

Question 1.
6 × 3 = 18
6 times as many as 3 is 18.

Question 2.
63 = 7 × 9

Answer: 63 is 7 times as many as 9.

Explanation:

Question 3.
5 × 4 = 20

Answer: 5 times as many as 4 is 20.

Explanation:

Question 4.
48 = 8 × 6

Answer: 48 is 6 times as many as 8.

Explanation:

Write an equation.

Question 5.
2 times as many as 8 is 16.

Answer: 2 × 8 = 16

Explanation:

Question 6.
42 is 6 times as many as 7.

Answer: 42 = 6 × 7

Explanation:

Question 7.
3 times as many as 5 is 15.

Answer: 3 × 5 = 15

Explanation:

Question 8.
36 is 9 times as many as 4.
Answer: 36 = 9 × 4

Explanation:

Question 9.
72 is 8 times as many as 9.
Answer: 72 = 8 × 9

Explanation:

Question 10.
5 times as many as 6 is 30.
Answer: 5 × 6 = 30

Explanation:

Problem Solving

Question 13.

Draw a model, and write an equation to represent “4 times as many as 3 is 12.” Explain your work.

Explanation:

### Common Core – Multiplication Comparisons – Lesson Check – Page No. 68

Question 1.
Which equation best represents the comparison sentence?
24 is 4 times as many as 6.
Options:
a. 24 × 4 = 6
b. 24 = 4 × 6
c. 24 = 4 + 6
d. 4 + 6 = 24

Explanation:

Question 2.
Which comparison sentence best represents the equation?
5 × 9 = 45
Options:
a. 5 more than 9 is 45.
b. 9 is 5 times as many as 45.
c. 5 is 9 times as many as 45.
d. 45 is 5 times as many as 9.

Explanation:

Spiral Review

Question 3.
Which of the following statements correctly compares the numbers?
Options:
a. 273,915 > 274,951
b. 134,605 < 143,605
c. 529,058 > 530,037
d. 452,731 > 452,819

Explanation: 134,605 is lesser compared to 143,605.

Question 4.
What is the standard form for
200,000 + 80,000 + 700 + 6?
Options:
a. 2,876
b. 28,706
c. 208,706
d. 280,706

Explanation: 200,000+80,000+700+6= 280,706.

Question 5.
Sean and Leah are playing a computer game. Sean scored 72,491 points. Leah scored 19,326 points more than Sean. How many points did Leah score?
Options:
a. 53,615
b. 91,717
c. 91,815
d. 91,817

Explanation: Sean’s score is 72,491 and Leah’s score is 19,326 more than Sean’s score. So Sean score is 72,491+19,326 = 91,817.

Question 6.
A baseball stadium has 38,496 seats. Rounded to the nearest thousand, how many seats is this?
Options:
a. 38,000
b. 38,500
c. 39,000
d. 40,000

Explanation: Round off to the nearest thousand is 38,000.

### Multiplication Comparisons – Page No. 71

Question 1.
Maria’s dog weighs 6 times as much as her rabbit. Together the pets weigh 56 pounds. What does Maria’s dog weigh? Draw a model. Let n represent the unknown.

Explanation: Let the weight of the rabbit be X and the dog’s weight is 6X. Both pet’s weight is 56 pounds i.e 6X+X=56, 7X=56 then X is 8.
Rabbit’s weight is 8 and Dog’s weight is 6×8= 48.

Draw a model. Write an equation and solve.

Practice: Copy and Solve Draw a model.
Write an equation and solve.

Question 4.
At the dog show, there are 4 times as many boxers as spaniels. If there are a total of 30 dogs, how many dogs are spaniels?

Explanation: Let spaniels be S and the boxers be 4S. As the total is 30, S+4S=30 then 5S=30.
Therefore S is 6. Spaniels are 6 and boxers are 4 times as many as spaniels. So boxers are 4×6=24.

Question 5.
There are 5 times as many yellow labs as terriers in the dog park. If there are a total of 18 dogs, how many dogs are terriers?

Explanation: Let the Terriers be T and yellow labs be 5T. As total dogs are 18, 5T+T=18, and therefore T=18/6 which is 3. Terriers are 3.

### Multiplication Comparisons – Page No. 72

Question 8.
To get to a dog show, Mr. Luna first drives 7 miles west from his home and then 3 miles north. Next, he turns east and drives 11 miles. Finally, he turns north and drives 4 miles to the dog show. How far north of Mr. Luna’s home is the dog show? To solve the problem, Dara and Cliff drew diagrams. Which diagram is correct? Explain.

Explanation: Mr. Luna’s travels east and west are irrelevant to the question. As he drives 3 miles north, then he drives 4 more miles north. 3 + 4 = 7, so Mr. Luna ends up 7 miles north of his home.

Question 9.
Use Reasoning Valerie and Bret have a total of 24 dog show ribbons. Bret has twice as many ribbons as Valerie. How many ribbons does each have?
Valerie’s ribbons: ______          Bret’s ribbons: ______

Answer: Valerie has 8 and Bret has 16.

Explanation: Let Valerie ribbons be X and Bret’s ribbons be 2X and the total be X+2X= 24. Therefore X= 8.
Valerie has 8 and Bret has 2×8= 16.

Question 10.
Noah built a fenced dog run that is 8 yards long and 6 yards wide. He placed posts at every corner and every yard along the length and width of the run. How many posts did he use?

Answer: 2×7+2×5+4(as he posted at every corner)= 14+10+4= 28 posts

Explanation: As there are 7 posts along one 8 yard side and 5 posts along one 6 yard side, so he used 2×7+2×5+4(as he posted at every corner)= 14+10+4= 28 posts

Question 11.
Last weekend, Mandy collected 4 times as many shells as Cameron. Together, they collected 40 shells. How many shells did Mandy collect? Complete the bar model. Then, write an equation and solve.

### Common Core – Comparison Problems – Page No. 73

Draw a model. Write an equation and solve.

Question 1.
Stacey made a necklace using 4 times as many blue beads as red beads. She used a total of 40 beads. How many blue beads did Stacey use?

Question 2.
At the zoo, there were 3 times as many monkeys as lions. Tom counted a total of 24 monkeys and lions. How many monkeys were there?
______ monkeys

Explanation:

Question 3.
Fred’s frog jumped 7 times as far as Al’s frog. The two frogs jumped a total of 56 inches. How far did Fred’s frog jump?

Explanation:

Question 4.
Sheila has 5 times as many markers as Dave. Together, they have 18 markers. How many markers does Sheila have?

Explanation: 15 markers.

Problem Solving

Question 7.
Write a problem involving how much more than and solve it. Explain how drawing a diagram helped you solve the problem.

Answer: Mike has 10 chocolates and John has 5 chocolates. How many more chocolates does Chirs have?
5 chocolates more Chirs have.

Explanation: As Mike has 10 chocolates and john has 5 chocolates, Chirs has 5 more chocolates than John.

### Common Core – Comparison Problems – Lesson Check – Page No. 74

Question 1.
Sari has 3 times as many pencil erasers as Sam. Together, they have 28 erasers. How many erasers does Sari have?
Options:
a. 7
b. 14
c. 18
d. 21

Explanation: Let the X be pencil erasers of Sam and Sari erasers be 3X. As Sari and Sam together have 28 erasers. So 3X+X= 28. And X is 7. Then Sari has 3×7= 21.

Question 2.
In Sean’s fish tank, there are 6 times as many goldfish as guppies. There are a total of 21 fish in the tank. How many more goldfish are there than guppies?
Options:
a. 5
b. 12
c. 15
d. 18

Explanation: Let Guppies be X and Goldfishes be 6X. And the total fishes are 21, So X+6X= 21 then X= 3.
So Goldfishes are 6×3= 18.

Spiral Review

Question 3.
Barbara has 9 stuffed animals. Trish has 3 times as many stuffed animals as Barbara. How many stuffed animals does Trish have?
Options:
a. 3
b. 12
c. 24
d. 27

Explanation: Barbara has 9 stuffed animals and Trish has 3 times as Barbara, So 9×3= 27.

Question 4.
There are 104 students in the fourth grade at Allison’s school. One day, 15 fourth-graders were absent. How many fourth-graders were at school that day?
Options:
a. 89
b. 91
c. 99
d. 119

Explanation: Total students in fourth grade are 104, as 15 students were absent 104-15= 89.

Question 5.
Joshua has 112 rocks. Jose has 98 rocks. Albert has 107 rocks. What is the correct order of the boys from the least to the greatest number of rocks owned?
Options:
a. Jose, Albert, Joshua
b. Jose, Joshua, Albert
c. Albert, Jose, Joshua
d. Joshua, Albert, Jose

Explanation: As 98<107<112. So Jose, Albert, Joshua.

Question 6.
Alicia has 32 stickers. This is 4 times as many stickers as Benita has. How many stickers does Benita have?
Options:
a. 6
b. 8
c. 9
d. 28

Explanation: Let Benita stickers be S and Alicia has 32 stickers, So 4×S= 32. Therefore Benita stickers are 8.

### Comparison Problems – Page No. 77

Question 1.
Use the drawing to find 2 × 500.

Explanation: 2×500 is 2 times 5 hundreds, which is equal to 10 hundreds and 10 hundreds are equal to 1000.

Complete the pattern.

Question 2.
3 × 8 = 2
i. 3 × 80 = _____
ii. 3 × 800 = _____
iii. 3 × 8,000 = _____

Explanation: 3×80= 240
3×800= 2400
3×8000= 24,000

Question 3.
6 × 2 = 12
i. 6 × 12 = _____
ii. 6 × 120 = _____
iii. 6 × 1,200 = _____

Explanation: 6×12= 72
6×120= 720
6×1200= 7200.

Question 4.
i. 4 × 5 = _____
ii. 4 × 50 = _____
iii. 4 × 500 = _____
iv. 4 × 5,000 = _____

Explanation: 4×5= 20
4×50= 200
4×500= 2000
4×5,000= 20,000.

Find the product.

Find the product.

Question 7.
7 × 6,000 = _____

Explanation:

Question 8.
4 × 80 = _____

Explanation:

Question 9.
3 × 500 = _____

Explanation:

Use Reasoning Algebra Find the missing factor.

Question 12.
8 × _____ = 3,200

Explanation: 8×4= 32.

Question 13.
Communicate How does the number of zeros in the product of 8 and 5,000 compare to the number of zeros in the factors? Explain.

Explanation: There are 4 zeros in the product and 3 zeros only in the factors. Because there is a zero in basic fact as 8×5=40.

### Comparison Problems – Page No. 78

Question 14.
Joe’s Fun and Sun rents beach chairs. The store rented 300 beach chairs each month in April and in May. The store rented 600 beach chairs each month from June through September. How many beach chairs did the store rent during the 6 months?
a. What do you need to know?

Answer: We need to know about the total number of beach chairs rented during the 6 months.

Question 14.
b. How will you find the number of beach chairs?

Answer: 300×2= 600 and 600×4= 2400. Total beach chairs are 3000

Explanation: We will multiply 2 times 300 and 4 times 600 and the will add the product.

Question 14.
c. Show the steps you use to solve the problem.

Answer: 300×2= 600 and 600×4= 2400. Total beach chairs are 3000.

Question 14.
d. Complete the sentences.
For April and May, a total of ______ beach chairs were rented.

Explanation: As the store rented 300 beach chairs in April and May, So 300×2= 600.

Question 14.
For June through September, a total of _____ beach chairs were rented.

Explanation: As the store rented 600 beach chairs from June to September, So 600×4= 2400.

Question 14.
Joe’s Fun and Sun rented _____ beach chairs during the 6 months.

Explanation: 300×2= 600 and 600×4= 2400. Total beach chairs are 3000.

Question 16.
Carmen has three books of 20 stamps and five books of 10 stamps. How many stamps does Carmen have? Complete the equation using the numbers on the tiles.

______ × 20 + ______ × 10 = ______

Explanation: 3×20+5×10= 110.

### Common Core – Multiply Tens, Hundreds, and Thousands – Page No. 79

Find the product.

Question 1.
4 × 7,000 = 28,000
Think: 4 × 7 = 28
So, 4 × 7,000 = 28,000

Question 2.
9 × 60 = _____

Explanation: 9×6= 54.

Question 3.
8 × 200 = _____

Explanation: 8×2=16

Question 4.
5 × 6,000 = _____

Explanation: 5×6=30.

Question 7.
6 × 3,000 = _____

Explanation: 6×3= 18.

Question 8.
3 × 8,000 = _____

Explanation: 3×8= 24.

Question 9.
5 × 500 = _____

Explanation: 5×5= 25.

Question 10.
9 × 4,000 = _____

Explanation: 9×4= 36.

Question 11.
7 × 7,000 = _____

Explanation: 7×7= 49.

Question 12.
3 × 40 = _____

Explanation: 3×4= 12.

Question 13.
4 × 5,000 = _____

Explanation: 4×5= 20.

Question 14.
2 × 9,000 = _____

Explanation: 2×9= 18.

Problem Solving

### Common Core – Multiply Tens, Hundreds, and Thousands – Lesson Check – Page No. 80

Question 1.
A plane is traveling at a speed of 400 miles per hour. How far will the plane travel in 5 hours?
Options:
a. 200 miles
b. 2,000 miles
c. 20,000 miles
d. 200,000 miles

Explanation: The speed of the plane is 400 miles per hour. In 5 hours plane can travel 400×5= 2,000 miles.

Question 2.
One week, a clothing factory made 2,000 shirts in each of 6 different colors. How many shirts did the factory make in all?
Options:
a. 2,000
b. 12,000
c. 120,000
d. 200,000

Explanation: Shirts made in one week are 2000 in 6 different colors. So total shirts made in all are 2000×6= 12,000.

Spiral Review

Question 3.
Which comparison sentence best represents the equation?
6 × 7 = 42
Options:
a. 7 is 6 times as many as 42.
b. 6 is 7 times as many as 42.
c. 42 is 6 times as many as 7.
d. 6 more than 7 is 42.

Explanation: By comparing 42= 6×7 represents the equation.

Question 4.
The population of Middleton is six thousand, fifty-four people. Which of the following shows this number written in standard form?
Options:
a. 654
b. 6,054
c. 6,504
d. 6,540

Explanation: Six thousand fifty-four is equal to 6,054.

Question 5.
In an election for mayor, 85,034 people voted for Carl Green and 67,952 people voted for Maria Lewis. By how many votes did Carl Green win the election?
Options:
a. 17,082
b. 17,182
c. 22,922
d. 152,986

Explanation: Total votes Carl Green got are 85,034and Maria Lewis got are 67,952. By 85,034-67,952= 17,082 votes Carl Green won the election.

Question 6.
Meredith picked 4 times as many green peppers as red peppers. If she picked a total of 20 peppers, how many green peppers did she pick?
Options:
a. 4
b. 5
c. 16
d. 24

Explanation: Let the red peppers be X and green peppers be 4X, And the total she picked is 20 peppers. So X+4X=20,
Then X=4. Green peppers she picked are 4×4= 16.

### Multiply Tens, Hundreds, and Thousands – Page No. 83

Tell whether the exact answer is reasonable.

Question 3.
Kira needs to make color copies of a horse show flyer. The printer can make 24 copies in 1 minute. Kira says the printer makes 114 copies in 6 minutes.

Explanation: As the printer can make 24 copies in 1 minute, So if we take 24 rounds off to 20 or 30 then the printer makes 120 or 180 copies. So Kira is incorrect.

Question 4.
Jones Elementary is having a car wash to raise money for a community horse trail. Each car wash ticket costs $8. Tiara says the school will receive$1,000 if 125 tickets are sold.

Explanation: As 1000÷125= 8 which is each car wash ticket cost. So the answer is reasonable.

Tell whether the exact answer is reasonable.

Question 5.
Evaluate Reasonableness Mrs. Hense sells a roll of coastal Bermuda horse hay for $58. She says she will make$174 if she sells 3 rolls.

Explanation: As 174 is the nearest rounding off to 180. So the answer is reasonable.

Question 6.
Mr. Brown sells horse supplies. A pair of riding gloves sells for $16. He says he will make$144 if he sells 9 pairs.

Explanation: As 144 is between 90 and 180, So the answer is reasonable. Here we will take rounding off for 9 as 10 and 20. So the answer must be between 90 and 180.

Question 7.
Path A and Path B are walking paths used for horses. Path A is 118 feet long. Path B is 180 feet long. Carlos walks his horse down each path 3 times. Which path did Carlos use to walk his horse about 500 feet? Explain.

Explanation: 118 is rounded off to 100 and then multiply with 3, 100  Then round off 180 to 200 and multiply with 3, 200  As 500 is closer to estimate of 600 compared to 300. So Path B is correct.

Question 8.
Students in the third grade sell 265 tickets to the school play. Students in the fourth grade sell 3 times as many tickets as the third-grade students. Estimate the number of tickets the fourth-grade students sold by finding the two numbers the exact answer is between.
The students sold between

Explanation: 1let 265 be rounded off 200 and 300. As fourth-grade students sell 3 times as many as third-grade students, So 200 and 300  So tickets sold between 600 and 900.

### Multiply Tens, Hundreds, and Thousands – Page No. 84

Predict whether the exact answer will be less than or greater than the estimate. Explain your answer.

Question 9.
The food stand at the zoo sold 2,514 pounds of hamburger last month. The average cost of a pound of hamburger is $2. Jeremy estimates that about$6,000 worth of hamburger was sold last month.

Answer: Lesser than the actual amount of hamburger.

Explanation: As the amount of hamburger sold is 468 pounds less than the estimated amount of 3000 pounds. So, the answer will be less than estimated.

Question 10.
A zoo bought 2,240 pounds of fresh food for the bears this month. The average cost of a pound of food is $4. Jeremy estimates that about$8,000 was spent on fresh food for the bears this month.

Answer: Greater than the actual amount of food bought.

Explanation: The actual amount of food bought for the bears this month was 240 pounds greater than the estimated amount of 2,000 pounds. So, the answer will be greater than the estimated amount.

### Common Core – Estimate Products – Page No. 85

Estimate the product by rounding.

Question 1.
4 × 472
4 × 472

4 × 500 = 2,000

Question 2.
2 × 6,254

Explanation: The nearest rounding off for 6,254 is 6,000. So 2×6,000= 12,000.

Question 6.
6 × 98

Answer: The nearest rounding off for 98 is 100. So 6×100= 600.

Question 7.
8 × 3,250

Answer: The nearest rounding off for 3,250 is 3,000. So 8×3,000= 24,000.

Question 8.
7 × 777

Explanation: The nearest rounding off for 777 is 800. So 7×800= 5,600.

Find two numbers the exact answer is between.

Question 9.
3 × 567

Explanation: The rounding off for 567 is 500 and 600. So 3×500= 1500 and 3×600= 1800.

Question 10.
6 × 7,381

Explanation: The rounding off for 7,381 is 7,000 and 8,000. So 6×7000= 42,000 and 6×8000= 48,000.

Question 11.
4 × 94

Explanation: The rounding off for 94 is 90 and 100. So 4×90= 360 and 4×100= 400.

Question 12.
6 × 684

Explanation: The rounding off for 684 is 600 and 700. So 6×600= 3600 and 6×700= 4200.

Problem Solving

### Common Core – Estimate Products – Lesson Check – Page No. 86

Question 1.
A theater has 4,650 seats. If the theater sells all the tickets for each of its 5 shows, how many tickets will the theater sell in all?
Options:
a. 2,500
b. 10,000
c. 25,000
d. 30,000

Explanation: The nearest round-off for 4,650 is 5,000. So 5,000×5= 25,000.

Question 2.
Washington Elementary has 4,358 students. Jefferson High School has 3 times as many students as Washington Elementary. About how many students does Jefferson High School have?
Options:
a. 16,000
b. 12,000
c. 10,000
d. 1,200

Explanation: As the nearest round off for 4,358 is 4,000. So 4,000×3= 12,000.

Spiral Review

Question 3.
Diego has 4 times as many autographed baseballs as Melanie has. Diego has 24 autographed baseballs. How many autographed baseballs does Melanie have?
Options:
a. 28
b. 20
c. 8
d. 6

Explanation: Let the Melanie baseballs be S. As Diego has 4 times as many as Melanie and Diego has a total of 24 baseballs. So 4×S= 24, Then S= 24÷4 which is 6.

Question 4.
Mr. Turkowski bought 4 boxes of envelopes at the office supply store. Each box has 500 envelopes. How many envelopes did Mr. Turkowski buy?
Options:
a. 200
b. 504
c. 2,000
d. 20,000

Explanation: Turkowski has 4 boxes of envelopes and each box contains 500 envelopes, So total envelopes did Turkowski bought are 4×500= 2,000.

Question 5.
Pennsylvania has a land area of 44,816 square miles. Which of the following shows the land area of Pennsylvania rounded to the nearest hundred?
Options:
a. 44,000 square miles
b. 44,800 square miles
c. 44,900 square miles
d. 45,000 square miles

Explanation: As the nearest round off for 44,816 is 44,800.

Question 6.
The table shows the types of DVDs customers rented from Sunshine Movie Rentals last year.

How many comedy and action movies were rented in all last year?
Options:
a. 13,620
b. 13,000
c. 12,260
d. 10,752

Explanation: Comedy and action movies that are rented in last year are 6,720+5,540= 12,260.

### Estimate Products – Page No. 89

Model the product on the grid. Record the product.

Question 1.
3 × 13

3 × 13 = _____

Explanation: 3×13= 3 ×(10+3)
=(3×10)+ (3×3)
=30+9
=39

Question 2.
5 × 14

5 × 14 = _____

Explanation: 5×14 = 5×(10+4)
= (5×10)+(5×4)
= 50+20
= 70

Find the product.

Question 3.
6 × 14

6 × 14 = ______

Explanation: 6×14= 6×(10+4)
= (6×10)+(6×4)
= 60+24
= 84

Question 4.
5 × 18

5 × 18 = ______

Explanation: 5 × 18 =5 ×(10+8)
= (5 × 10)+ (5 ×8)
= 50+40
= 90.

Question 5.
4 × 16

4 × 16 = ______

Explanation: 4 × 16= (4 × 10)+( 4 ×6)
= 40+24
= 64.

Use grid paper or base-ten blocks to model the product.
Then record the product.

Question 8.
9 × 13 = ______

Explanation: 9 × 13 = 9 ×(10+3)
=(9×10)+(9×3)
=90+27
=117

Question 9.
Explain how modeling partial products can be used to find products of greater numbers.

=(20×3)+(5×3)= 60+15=75

Explanation: Multiplication is easy. For example, if we take 25 3= (20+5) 3
=(20×3)+(5×3)= 60+15=75

Question 10.
Use the Distributive Property to model the product on the grid. Record the product.
4 × 14 = _____

Explanation: 4×14= 4×(10+4)
=(4×10)+(4×4)
=40+16
=56

### Estimate Products – Page No. 90

Question 11.
Kyle went to a fruit market. The market sells a wide variety of fruits and vegetables. The picture at the right shows a display of oranges. Write a problem that can be solved using the picture.

Answer: A shopkeeper has oranges. He keeps his oranges in the basket having 6 rows and each row has 12 oranges. So how many oranges he owned.

Explanation: From the above picture we can see 6 rows and 12 columns of Oranges.
So total no. of Oranges are 6 12= 72 Oranges.

Question 12.
Describe how you could change the problem by changing the number of rows of oranges and the number of empty spaces in the picture. Then solve the problem.

### Common Core – Multiply Using the Distributive Property – Page No. 91

Model the product on the grid. Record the product.

Question 1.
4 × 19 = 76

4 × 10 = 40 and 4 × 9 = 36
40 + 36 = 76

Question 2.

5 × 13 = ______

Explanation:
5×10= 50 and 5×3= 15
50+15= 65.

Find the product.

Question 3.

4 × 14 = ______

Explanation:
4×10= 40 and 4×4= 16
40+16= 56.

Question 4.

3 × 17 = ______

Explanation:
3×10=30 and 3×7= 21
30+21= 51

Question 5.

6 × 15 = ______

Explanation:
6×10= 60 and 6×5= 30
60+30= 90

Problem Solving

Question 6.
Michael arranged his pennies in the following display.

How many pennies does Michael have in all?

Explanation: As there are 7 columns and 13 rows, So 13×7= 91.

Question 7.
A farmer has an apple orchard with the trees arranged as shown below.

If the farmer wants to pick one apple from each tree, how many apples will he pick?

Explanation: As there are 5 columns and 14 rows, So 5×14= 70.

### Common Core – Multiply Using the Distributive Property – Lesson Check – Page No. 92

Question 1.
The model shows how Maya planted flowers in her garden.

How many flowers did Maya plant?
Options:
a. 15
b. 18
c. 30
d. 45

Explanation: As 3×10= 30 and 3×5= 15
30+15= 45.

Question 2.
The model below represents the expression 5 x 18.

How many tens will there be in the final product?
Options:
a. 5
b. 6
c. 8
d. 9

Explanation: As 5×18 is 90 and 90÷10= 9. So answer is 9.

Spiral Review

Question 3.
Center City has a population of twenty one thousand, seventy people. Which of the following shows the population written in standard form?
Options:
a. 21,007
b. 21,070
c. 21,077
d. 21,700

Explanation: Twenty-one thousand seventy is equal to 21,070.

Question 4.
Central School collected 12,516 pounds of newspaper to recycle. Eastland School collected 12,615 pounds of newspapers. How many more pounds of newspaper
did Eastland School collect than Central School?
Options:
a. 99 pounds
b. 101 pounds
c. 199 pounds
d. 1,099 pounds

Explanation: Central school has collected 12,516 pounds and Eastland school collected 12,615 pounds. So
12,615-12,516= 99.

Question 5.
Allison has 5 times as many baseball cards as football cards. In all, she has 120 baseball and football cards. How many baseball cards does Allison have?
Options:
a. 20
b. 24
c. 96
d. 100

Explanation: Let Football cards be X and baseball cards be 5X. So 5X+X= 120 in which X= 20. As Allison has 5 times as many baseball cards as football cards. So 5×20= 100.

Question 6.
A ruby-throated hummingbird beats its wings about 53 times each second. About how many times does a ruby-throated hummingbird beat its wings in 5 seconds?
Options:
a. 25
b. 58
c. 250
d. 300

Explanation: As the nearest round-off for 53 is 50, So 50×5= 250.

### Multiply Using the Distributive Property – Page No. 95

Question 1.
Find 4 × 213. Use expanded form.

_____

Record the product. Use expanded form to help.

Record the product. Use expanded form to help.

Question 4.
4 × 21 = _____

Explanation: 4×(20+1)
= (4×20)+(4×1)
= 80+4
= 84.

Question 5.
6 × 35 = _____

Explanation: 6×(30+5)
= (6×30)+(6×5)
= 180+30
= 210.

Question 6.
A hotel has 128 rooms on each floor. There are 4 floors in all. If 334 of the rooms in the hotel have been cleaned, how many rooms still need to be cleaned?

Explanation: Total floors in a hotel are 4 and each floor has 128 rooms, So total rooms in the hotel are 128×4= 512.
In 512 rooms 334 were cleaned and the remaining rooms yet to be cleaned are 512-334= 178.

Question 7.
Ben wants to buy 2 blue sweaters for $119 each and 3 brown sweaters for$44 each. How much will Ben spend on the five sweaters?

Answer: $370. Explanation: Ben wants to buy 2 blue sweaters for$119 each, So 119×2= 238. And 3 brown sweater for $44 each which means 44×3= 132. The total he spent on five sweaters is 238+132= 370. Question 8. A jeweler has 36 inches of silver chain. She needs 5 times that much to make some necklaces and 3 times that amount to make some bracelets. How much silver chain does the jeweler need to make her necklaces and bracelets? Answer: 288 inches. Explanation: As the jeweler has 36 inches of silver chain and she needs 5 times to make some necklaces which means 36×5= 180 and 3 times to make a bracelet which means 36×3= 108. So the total sliver she needs is 180+108= 288. Question 9. Gretchen walks her dog 3 times a day. Each time she walks the dog, she walks 1,760 yards. How many yards does she walk her dog in 3 days? Answer: 15,840 yards. Explanation: Gretchen walks 3 times a day which means for 3 days it will be 9 times. As she walks 1,760 yards, So 1760×9= 15,840. Question 10. Write an Expression Which expression could you write to show how to multiply 9 × 856 using place value and expanded form? Answer: (9×800)+(9×50)+(9×6) Explanation: Place value is the value of each digit in a number. So 856 can be expanded as 800+50+6. Question 11. Jennifer bought 4 packages of tacks. There are 48 tacks in a package. She used 160 of the tacks to put up posters. How many tacks does she have left? Explain. Answer: 32. Explanation: Jennifer bought 4 packages of tacks and each package contains 48 tacks. So total tacks are 48×4= 192. As she used 160 tacks total tacks she left are 192-160= 32 ### Multiply Using the Distributive Property – Page No. 96 Use the table for 12–13. Question 12. What is the total cost of 3 Italian cypress trees? Answer:$237.

Explanation: The cost of each Italian cypress tree is $79. The total cost of 3 Italian cypress trees is 79×3= 237. Question 13. What’s the Error? Tanya says that the difference in the cost of 4 flowering cherry trees and 4 Muskogee crape myrtles is$80. Is she correct? Explain.

Answer: No, Because she used a normal price instead of the discounted price.

Explanation: For 4 and above trees, there is a discount price. So she is wrong.

Question 14.
What is the greatest possible product of a 2-digit number and a 1-digit number? Explain how you know.

Explanation: The greatest 2-digit number is 99 and the greatest single-digit number is 9. So the product is
99×9= 891.

Question 15.
Multiply 5 × 381 using place value and expanded form. Select a number from each box to complete the expression.

Explanation: The expanded form of 381 is 300+80+1.

### Common Core – Multiply Using Expanded Form – Page No. 97

Record the product. Use expanded form to help.

Question 1.
7 × 14 = 98
7 × 14 = 7 × (10 + 4)
= (7 × 10) + (7 × 4)
= 70 + 28
= 98

Question 2.
8 × 43 = _____

Explanation: 8×(40+3)
= (8×40)+(8×3)
= 320+24
= 344.

Question 5.
4 × 2,371 = _____

Explanation: 4×2,371= 4×(2000+300+70+1)
= (4×2,000)+(4×300)+(4×70)+(4×1)
=8000+1200+280+4
=9,484

Question 6.
7 × 1,829 = _____

Explanation: 7×1,829= 7×(1,000+800+20+9)
=(7×1,000)+( 7×800)+( 7×20)+( 7×9)
=7,000+5600+140+63
=12,803

Problem Solving

Question 7.
The fourth-grade students at Riverside School are going on a field trip. There are 68 students on each of the 4 buses. How many students are going on the field trip?

Explanation: No. of buses is 4 and on each bus, there are 68 students. So 68 4= 272.

### Common Core – Multiply Using Expanded Form – Lesson Check – Page No. 98

Question 1.
Which expression shows how to multiply 7 × 256 by using expanded form and the Distributive Property?
Options:
a. (7 × 2) + (7 × 5) + (7 × 6)
b. (7 × 200) + (7 × 500) + (7 × 600)
c. (7 × 2) + (7 × 50) + (7 × 600)
d. (7 × 200) + (7 × 50) + (7 × 6)

Explanation: By Distributive property of multiplication 7×256=(7×200)+(7×50)+(7×6)

Question 2.
Sue uses the expression (8 × 3,000) + (8 × 200) + (8 × 9) to help solve a multiplication problem. Which is Sue’s multiplication problem?
Options:
a. 8 × 329
b. 8 × 3,029
c. 8 × 3,209
d. 8 × 3,290

Explanation: The expression (8×3,000)+(8×200)+(8×9) is written in the Distributive property of multiplication. So 8×3,029.

Spiral Review

Question 3.
What is another way to write 9 × 200?
Options:
a. 18 ones
b. 18 tens
c. 18 hundreds
d. 18 thousands

Explanation: 9×200= 1800

Question 4.
What is the value of the digit 4 in 46,000?
Options:
a. 4 ten thousands
b. 4 thousands
c. 4 hundreds
d. 4 tens

Explanation: The place value of 4 in 46,000 is 40,000.

Question 5.
Chris bought 6 packages of napkins for his restaurant. There were 200 napkins in each package. How many napkins did Chris buy?
Options:
a. 120
b. 1,200
c. 12,000
d. 120,000

Explanation: Total packages are 6 and each package contains 200 napkins. So 6 200=1,200.

Question 6.
Which of the following lists the numbers in order from least to greatest?
Options:
a. 8,512; 8,251; 8,125
b. 8,251; 8,125; 8,512
c. 8,125; 8,512; 8,251
d. 8,125; 8,251; 8,512

Explanation: 8,125>8,251>8,512.

### Multiply Using Expanded Form – Page No. 101

Question 1.
Use the model to find 2 × 137.

Explanation: 2×137= 2×(100+30+7)
=(2×100)+(2×30)+(2×7)
=200+60+14
=274.

Estimate. Then record the product.

Question 2.
1 9 0
×   3
———–
Estimate: ________
Product: ________

Estimate: 600
Product: 570.

Explanation: Round off 190 to 200 and 200×3= 600. And the product is 190×3= 570.

Question 3.
4 7 1
×   4
———–
Estimate: ________
Product: ________

Estimate: 2000
Product: 1884.

Explanation: Round off 471 to 500 and 500×4= 2000. And the product is 471×4= 1884.

Question 4.
3, 439
×     7
———–
Estimate: ________
Product: ________

Estimate: 24,500
Product: 24,073.

Explanation: Round off 3,439 to 3500 and 3500×7= 24,500. And the product is 35000×7= 24,073.

Estimate. Then record the product.

Question 7.
6 0 8
×    6
———–
Estimate: ________
Product: ________

Estimate: 4,200
Product: 3,648

Explanation: Round off 608 to 700 and 700×6= 4,200. And the product is 608×6= 3,648.

Practice: Copy and Solve Estimate. Then record the product.

Question 8.
2 × 78 =
Estimate: ________
Product: ________

Estimate: 200
Product: 156

Explanation: Round off 78 to 100 and 100×2= 200. And the product is 78×2= 156.

Question 9.
2 × $210 = Estimate:$ ________
Product: $________ Answer: Estimate:$600
Product: $420 Explanation: Round off 210 to 300 and 300×2= 600. And the product is 210×2= 420. Question 10. 2 ×$682 =
Estimate: $________ Product:$ ________

Estimate: $1,400. Product:$1,364

Explanation: Round off 682 to 700 and 700×2= 1400. And the product is 682×2= 1364.

Question 11.
8 × 8,145 =
Estimate: ________
Product: ________

Estimate: 68,000.
Product: 65,160.

Explanation: Round off 8,145 to 8,500 and 8,500×8= 68,000. And the product is 8145×8= 65,160.

Use Reasoning Algebra Find the missing digit.

Question 12.
■5
× 7
————-
455
■ = _____

Explanation: 65×7= 455.

Question 13.
2 4 8
×   3
————-
■ 44
■ = _____

Explanation: 248×3= 744

Question 14.
$3 9 5 × ■ ————$2,370
■ = _____

Explanation: 395×6= 2370

Question 15.
3,748
×    4
———-
1 ■,992
■ = _____

Explanation: 3,748×4= 14,992

Question 16.
A store bought 9 cases of light bulbs in May and 8 cases in June. There are 48 light bulbs in a case. How many light bulbs did the store buy in May and June?

Explanation: Light bulbs in May are 9 cases and in June are 8 cases. And each case have 48 light bulbs. So 9×48= 432 in May and 8×48= 384 in June. So total light bulbs in May and June are 384+432= 816.

Question 17.
Mr. Wilson saved $2,500 to buy airline tickets for his family. He bought 6 airline tickets for$372 each. How much of his savings does Mr. Wilson have after he buys the tickets?

Answer: $268. Explanation: Mr. Wilson bought 6 tickets and each costs$372, So 372×6= 2,232. Total money Mr. Wilson saved is $2,500. Total Savings are 2500-2232=$268.

Question 18.
Coach Ramirez bought 8 cases of bottled water for a road race. There are 24 bottles in each case. After the race, 34 bottles of water were left. How many bottles were used at the race? Explain.

Explanation: Ramirez bought 8 cases of water and each case contains 24 bottles. So total bottles are 8×24=192 and 34 bottles left. Therefore used bottles are 192-34= 158.

### Multiply Using Expanded Form – Page No. 102

Question 19.
Use Diagrams Look at the picture. Kylie has 832 songs on her portable media player. Lance has 3 times as many songs. How many fewer songs can Lance add to his player than Kylie can add to hers?

Explanation: Total songs in portable media players are 9,000, And kylie has 832 songs. So Kylie can add 9000-832= 8,168 songs. Lance has 3 times as many songs as Kylie, So Lance has 832×3= 2,496. He can add 9000-2496= 6504 to his player. Therefore 8168-6504=1664 Lance can add 1664 fewer songs to his player than Kylie.

Question 20.
James wants to buy the new portable media player shown. He has 5 times as many songs as Susan. Susan has 1,146 songs. Will all of his songs fit on the portable media player? How many songs does James have?

Answer: 5,730 songs. Yes, will fit on the portable media player.

Explanation: Susan has 1,146 songs and James has 5 times as many songs as Susan, So 1,146 5= 5,730 songs will fit on the portable media player.

Question 21.
The sum of a 3-digit number and a 1-digit number is 217. The product of the numbers is 642. If one number is between 200 and 225, what are the numbers?

Explanation: As the given product is 642 and the 3 digit number is between 200 and 225, So the 1 digit number is 3 because if we multiply 200 and 225 by 3 we will get the product as 600 and 675 and 642 is in between them. So 642 3= 214. And the one-digit number is 3.

Question 22.
Mrs. Jackson bought 6 gallons of juice for a party. Each gallon has 16 cups. After the party, 3 cups of juice were left over. At the party, how many cups did people drink? Show your work and explain how you found your answer.

Explanation: Mrs. Jackson bought 6 gallons of juice and each gallon has 16 cups. So total cups of juice is 16 6= 96 cups. And in that 3 cups of juice was left after the party. So 96-3= 93 cups of juice people drank.

### Common Core – Multiply Using Partial Products – Page No. 103

Estimate. Then record the product.

Question 1.
Estimate: 1,200
2 4 3
×   6
——————
1,200
2 4 0
+1 8
—————–
1,458

Question 2.
6 4 0
×   3
——————
Estimate: _________
Product: _________

Estimate: 1800
Product: 1920.

Explanation: Rounding off 640 to 600 then estimated product is 600 3= 1800 and 640 3= 1920.
6 4 0
×   3
——————
1800
+120
+0
——————
1920

Question 3.
$1 4 9 × 5 —————— Estimate:$ _________
Product: $_________ Answer: Estimate:$500
Product: $745 Explanation: Rounding off 149 to 100 then estimated product is 100 5= 500 and 149 5= 745.$ 1 4 9
×      5
——————
500
+200
+45
——————
745

Question 4.
7 2 1
×   8
——————
Estimate: _________
Product: _________

Estimate: 5600
Product: 5768

Explanation: Rounding off 721 to 700 then estimated product is 700 8= 5600 and 721 8= 5,768.
7 2 1
×   8
——————
5600
+160
+8
——————
5,768

Question 5.
2 9 3
×   4
——————
Estimate: _________
Product: _________

Estimate: 1,200
Product: 1,172

Explanation: Rounding off 293 to 300 then estimated product is 300 4= 1200 and 293 4=1,172.
2 9 3
×   4
——————
800
+360
+12
——————
1,172

Question 6.
$4 1 6 × 6 —————— Estimate:$ _________
Product: $_________ Answer: Estimate:$2400
Product: $2496 Explanation: Rounding off 293 to 300 then estimated product is 400 6= 2400 and 416 6= 2496.$ 4 1 6
×      6
——————
2400
+60
+36
—————–
2,496

Question 7.
9 6 1
×    2
——————
Estimate: _________
Product: _________

Estimate: 2000
Product: 1922

Explanation: Rounding off 961 to 1000 then estimated product is 1000 2= 2000 and
961 2= 1922.
9 6 1
×    2
——————
1800
+120
+2
——————-
1922

Question 8.
8 3 7
×   9
——————
Estimate: _________
Product: _________

Estimate: 7,200
Product: 7,533

Explanation: Rounding off 837 to 800 then estimated product is 800 9= 7200 and
837 9= 7533.

8 3 7
×   9
——————
7200
+270
+63
—————–
7533

Question 9.
6 5 2
×   4
——————
Estimate: _________
Product: _________

Estimate: 2,800
Product: 2,608

Explanation: Rounding off 652 to 700 then estimated product is 700 4= 2800 and
652 4= 2,608.
6 5 2
×   4
——————
2400
+200
+8
—————–
2608

Question 10.
3 0 7
×   3
——————
Estimate: _________
Product: _________

Estimate: 900
Product: 921

Explanation: : Rounding off 307 to 300 then estimated product is 300 3= 900 and
307 3= 921.
3 0 7
×   3
——–
900
+21
——
921

Question 11.
5 4 3
×   7
——————
Estimate: _________
Product: _________

Estimate: 3500
Product: 3,801

Explanation: : Rounding off 543 to 500 then estimated product is 500 7= 3500 and
543 7= 3801.
5 4 3
×   7
——————
3500
+280
+21
—————–
3801

Question 12.
$8 2 2 × 5 —————— Estimate:$ _________
Product: $_________ Answer: Estimate:$4,000.
Product: $4,110. Explanation: Explanation: : Rounding off 822 to 800 then estimated product is 800 5= 4000 and 822 5= 4110.$ 8 2 2
×      5
——————
4000
+100
+10
——————
4110

Problem Solving

Question 13.
A maze at a county fair is made from 275 bales of hay. The maze at the state fair is made from 4 times as many bales of hay. How many bales of hay are used for the maze at the state fair?

Explanation: No. of country fair bales are 275 and state fair bales are 4 times as many as country fair bales. So 275 4= 1100

### Common Core – Multiply Using Partial Products – Lesson Check – Page No. 104

Question 1.
A passenger jet flies at an average speed of 548 miles per hour. At that speed, how many miles does the plane travel in 4 hours?
Options:
a. 2,092 miles
b. 2,112 miles
c. 2,192 miles
d. 2,480 miles

Explanation: Average speed of passenger jet is 548 miles per hour. And the plane travels in 4 hours is 548 4= 2,192 miles.

Question 2.
Use the model to find 3 x 157.

Options:
a. 300,171
b. 300,157
c. 471
d. 451

Explanation: By distributive property of multiplication 3 x 157= 3 x(100+50+7)
=(3 x100)+(3×50)+(3×7)
=300+150+21
=471

Spiral Review

Question 3.
The school fun fair made $1,768 on games and$978 on food sales. How much money did the fun fair make on games and food sales?
Options:
a. $2,636 b.$2,646
c. $2,736 d.$2,746

Answer: $2746. Explanation: Money made on games is$1,768 and on food sale is $978. So total money make on games and food sales are 1768+978= 2746. Question 4. Use the table below. Which of the following lists the states from least to greatest population? Options: a. Alaska, North Dakota, Vermont b. Vermont, Alaska, North Dakota c. North Dakota, Vermont, Alaska d. Vermont, North Dakota, Alaska Answer: d. Explanation: Vermont has 621,760, North Dakota has 646,844 and Alaska has 698,473. So Vermont, North Dakota, Alaska. Question 5. A National Park covers 218,375 acres. What is this number written in expanded form? Options: a. 200,000 + 10,000 + 8,000 + 300 + 70 + 5 b. 20,000 + 1,000 + 800 + 30 + 75 c. 218 + 375 d. 218 thousand, 375 Answer: a. Explanation: 218,375 is expanded as 200,000 + 10,000 + 8,000 + 300 + 70 + 5 Question 6. Last year a business had profits of$8,000. This year its profits are 5 times as great. What are this year’s profits?
Options:
a. $4,000 b.$40,000
c. $44,000 d.$400,000

Explanation: Last year’s profit of $8,000 and this year 5 times more. So this year profit is 8000 5= 40,000. ### Multiply Using Partial Products – Page No. 105 Choose the best term from the box to complete the sentence. Question 1. To find the product of a two-digit number and a 1-digit number, you can multiply the tens, multiply the ones, and find the sum of each ________________. Answer: Factor Explanation: Factors are the numbers which divides the original number completely. Question 2. The _____________ states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. Answer: Distributive Property Explanation: Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. Write a comparison sentence. Question 3. 5 × 9 = 45 ______ times as many as ______ is ______ . Answer: 5 times as many as 9 is 45 Explanation: Question 4. 24 = 6 × 4 ______ is ______ times as many as ______ . Answer: 24 is 6 times as many as 4. Explanation: Question 5. 54 = 6 × 9 ______ is ______ times as many as ______ . Answer: 54 is 6 times as many as 9 Explanation: Question 6. 8 × 6 = 48 ______ times as many as ______ is ______ . Answer: 48 is 8 times as many as 6. Explanation: Estimate. Then record the product. Question 9. 2 8 × 3 ————— Answer: Estimate: 90 Product: 84 Explanation: Rounding off 28 to 30 estimated value is 30×3= 90 and 28×3= 84 Question 10.$4 3
× 6
—————
Estimate: $________ Product:$ ________

Estimate: 300
Product: 258

Explanation: Rounding off 43 to 50 estimated value is 50×6= 300 and 43×6= 258

Record the product. Use expanded form to help.

### Multiply Using Partial Products – Page No. 106

Question 13.
There are 6 times as many dogs as cats. If the total number of dogs and cats is 21, how many dogs are there?

Explanation: Let cats be X and dogs are as many as 6 so dogs be 6X. As the total number of cats and dogs are X+6X=21, And X= 3 so dogs are 6×3= 18

Question 14.
The table below shows the number of calories in 1 cup of different kinds of berries. How many calories are in 4 cups of blackberries?

Explanation: The number of calories of blackberries in one cup are 62 and in 4 cups are 62×4= 248.

Question 15.
The skating rink rented 218 pairs of skates during the month of April and 3 times that many in May. How many pairs of skates did the skating rink rent during April and May?

Explanation: No. of pairs of skates in April are 218 and 3 times that many in May. So
3×218= 654. Total skates in April and May are 218+654= 872

### Multiply Using Partial Products – Page No. 109

Question 1.
Break apart the factor 112 to find 7 × 112 by using mental math and addition.
7 × 112 = 7 × (_____ + 12)

Explanation: 7 × 112 = 7 × (100 + 12)
= 7×(100+12)
= 700+84
= 784

Find the product. Tell which strategy you used.

Question 4.
6 × 298 = _____

Explanation: 6×298 = 6×(200+90+8)
= (6×200)+( 6×90)+( 6×8)
= 1200+540+48
= 1788

Find the product. Tell which strategy you used.

Question 5.
14 × 50 = _____

Explanation: 14×50= (14×25)+(7×50)
= 350+350
= 700

Question 6.
32 × 25 = _____

Explanation: 32 × 25= 32× (20+5)
=(32×20)+(32×5)
=640+160
=800

Question 7.
8 × 25 × 23 = _____

Explanation: 8×25×23=(8×25)× 23
=(200) ×23
4,600

Practice: Copy and Solve Use a strategy to find the product.

Question 8.
16 × 400 = _____

Explanation: 16×400= (8+8)×400
=(8×400)+ (8×400)
=3200+3200
=6400

Question 9.
3 × 31 × 10 = _____

Explanation: 3×31×10= (3×31)×10
=(93) ×10
=930

Question 10.
3 × 199 = _____

Explanation: 3×199=3×(100+90+9)
=(3×100)+(3×90)+(3×9)
=300+270+27
= 597

Question 11.
3 × 1,021 = _____

Explanation: 3×1021= 3×(1000+20+1)
=(3×1000)+(3×20)+(3×1)
=3000+60+3
=3063

Identify Relationships Algebra Use mental math to find the unknown number.

Question 14.
The science museum sells dinosaur models to schools and libraries for $107 each. The town library buys 3 models. The town elementary school buys 5 models. What is the total cost of the models the town buys? Answer:$856.

Explanation: The cost of each dinosaur model is $107, And the town library buys 3 models which cost 107×3= 321, and town elementary school buys 5 models which cost 107×5= 535. Total cost is 321+535= 856. Question 15. Kyle and Karen each bought 6 books of ride tickets at the fair. Each book has 15 tickets. How many tickets did they buy altogether? Answer: 180 tickets Explanation: Kyle and Karen each bought 6 books each that means total of 12 books and each book has 15 tickets. So total tickets both bought are 12×15= 180 ### Multiply Using Partial Products – Page No. 110 Use the table for 16–18. Question 16. Three thousand, forty-three people buy tickets at the gate for Section N and one hundred people buy tickets at the gate for Section L. How much money is collected for Section N and Section L at the gate? Answer:$79575.

Explanation: As 3043 people bought tickets at the gate for Section N, So 3043×25= $76075 and 100 people bought tickets at the gate for Section L, So 100×35=$3500. The total money collected by both sections is 76075+3500= 79575.

Question 17.
Use Diagrams Tina and 3 of her friends buy the full season plan for Section M. If there are 45 games in the full season, how much money do they spend?

Answer: $4500. Explanation: Tina and 3 of her friends which means a total of 4 members bought full season for Section M which costs$25 for each, So total cost is 25×4= 100. If there are 45 games in full seasons then 45×100= $4500. Question 18. When the full season tickets first went on sale, 2,000 Full Season tickets sold for Section N. Two weeks after the tickets first went on sale, another 1,500 full season tickets were sold for Section N. How much money was spent on full season tickets for Section N in total? How much more money was spent when the tickets first went on sale than after the first two weeks?$ _____ was spent on full season tickets for Section N in total;

Answer: $70,000.$10,000 more

Explanation: The first sale tickets sold are 2,000 for Section N which is 2,000×20= 40,000.
And in next sale 1500 tickets sold out which is 1500×20= 30,000. Total money spent are 40,000+30,000= 70,000.

Question 19.
Find 6 × 407. Show your work and explain why the strategy you chose works best with the factors.

Explanation: By using Distributive property 6×407= 6×(400+7)
=(6×400)+(6×7)
=2400+42
=2,442.

### Common Core – Multiply Using Mental Math – Page No. 111

Find the product. Tell which strategy you used.

Question 1.
6 × 297
Think: 297 = 300 – 3
6 × 297 = 6 × (300 – 3)
= (6 × 300) – (6 × 3)
= 1,800 – 18
= 1,782;
use subtraction

Question 2.
8 × 25 × 23 = _____

Explanation: Associative property states that the terms in an addition or multiplication problem can be grouped in different ways, and the answer remains the same.
8 × 25 × 23= (8×25)×23
=200×23
=4600

Question 5.
9 × 199 = _____

Explanation: By Distributive property 9 × 199= 9 ×(100+90+9)
=(9×100)+(9×90)+(9×9)
=900+810+81
= 1791

Question 6.
20 × 72 × 5 = _____

Explanation: Associative property states that the terms in an addition or multiplication problem can be grouped in different ways, and the answer remains the same.
20 × 72 × 5= (20×72) ×5
=1440×5
=7,200.

Question 7.
32 × 25 = _____

Explanation: Multiplication.
32×25= 800.

Problem Solving

Question 8.
Section J in an arena has 20 rows. Each row has 15 seats. All tickets cost $18 each. If all the seats are sold, how much money will the arena collect for Section J? Answer:$5400.

Explanation: Total rows in the arena are 20 rows and each row has 15 seats. So total seats are 20×15= 300 seats. And each ticket cost is $18, So the total ticket price is 300×15= 5400. Question 9. At a high-school gym, the bleachers are divided into 6 equal sections. Each section can seat 395 people. How many people can be seated in the gym? Answer: 2,370 people. Explanation: Total sections are 6 and each section contains 395 people. So total members can be seated in the gym are 395×6= 2,370 people. ### Common Core – Multiply Using Mental Math – Lesson Check – Page No. 112 Question 1. Pencils come in cartons of 24 boxes. A school bought 50 cartons of pencils for the start of school. Each box of pencils cost$2. How much did the school spend
on pencils?
Options:
a. $240 b.$1,200
c. $2,400 d.$4,800

Explanation: Total boxes of pencils are 24 and a school bought 50 cartons of pencils. So total no. of boxes are 24×50=1200 and each box of pencils cost $2. So 1200×2= 2400 school has spent. Question 2. The school also bought 195 packages of markers. There are 6 markers in a package. How many markers did the school buy? Options: a. 1,170 b. 1,195 c. 1,200 d. 1,230 Answer: a Explanation: The school bought 195 packages of markers and each package contains 6 markers, So total markers are 195×6= 1170 Spiral Review Question 3. Alex has 175 baseball cards. Rodney has 3 times as many baseball cards as Alex. How many fewer cards does Alex have than Rodney? Options: a. 700 b. 525 c. 450 d. 350 Answer: d Explanation: Alex has 175 baseball cards and Rodney has 3 times as many as Alex, So total no. of cards Rodney have are 175×3= 525. And Alex has 525-175= 350 fewer cards than Rodney. Question 4. A theater seats 1,860 people. The last 6 shows have been sold out. Which is the best estimate of the total number of people attending the last 6 shows? Options: a. fewer than 6,000 b. about 6,000 c. fewer than 12,000 d. more than 20,000 Answer: c Explanation: No. of seats in a theater are 1,860 people and last 6 shows have been sold out, So 1,860×6= 11,160 which are fewer than 12,000. Question 5. At one basketball game, there were 1,207 people watching. At the next game, there were 958 people. How many people in all were at the two games? Options: a. 2,155 b. 2,165 c. 2,265 d. 10,787 Answer: b Explanation: There are 1207 people are watching basketball game and in the next game 958 people are there. So total no. of people are 1,207+958= 2165. Question 6. Bill bought 4 jigsaw puzzles. Each puzzle has 500 pieces. How many pieces are in all the puzzles altogether? Options: a. 200 b. 900 c. 2,000 d. 20,000 Answer: c Explanation: Bill bought 4 jigsaw puzzle and each puzzle has 500 pieces. So altogether pieces are 500×4= 2000. ### Multiply Using Mental Math – Page No. 115 Question 1. The seats in Sections A and B of the stadium are all taken for the last show. Section A has 8 rows of 14 seats each. Section B has 6 rows of 16 seats each. How many people are seated in Sections A and B for the last show? First, draw and label a diagram. Next, find the number of seats in each section. Last, find the total number of seats. _____ + _____ = _____ Answer: 112+96= 208. Explanation: As section A has 8 rows and 14 seats each, So 14×8= 112 and Section B has 6 rows and 16 seats each, So 16×6= 96. Total no. of people are seated in Section A and Section B are 112+96= 208. Question 1. There are _____________ people seated in Sections A and B for the last show. Answer: 208. Explanation: As Section A has 112 people and Section B has 96 people, So 112+96= 208. Question 2. What if Sections A and B each had 7 rows? How many people would have been seated in Sections A and B? Answer: 210 Explanation: As section A has 7 rows and 14 seats each, So 14×7= 98 and Section B has 7 rows and 16 seats each, So 16×7= 112. Total no. of people are seated in Section A and Section B are 112+98= 210. Question 3. Brenda’s vegetable garden has 13 rows with 8 plants in each row. Brenda plans to plant peppers in the first 2 rows and the last 2 rows of the garden. The rest of the rows will be tomatoes. How many tomato plants will Brenda plant? Answer: 72 tomato plants Explanation: Brenda’s vegetable garden has 13 rows with 8 plants in each row as she plans to plant first 2 rows and last 2 rows with pepper, So 13-4= 9 rows contains tomato plants and each row contains 8 plants, So 9×8= 72 tomato plants. Question 4. There are 8 rows of 22 chairs set up for an awards ceremony at the school. In each row, the 2 chairs on each end are reserved for students receiving awards. The rest of the chairs are for guests. How many chairs are there for guests? Answer: 144 Chairs. Explanation: As there are 8 rows with 22 chairs in each row, So total no. of chairs is 22×8= 176 chairs. As 2 chairs at each end are reserved for students receiving the award, So total chairs reserved are 8×4=32. So remaining chairs are 176-32= 144. ### Multiply Using Mental Math – Page No. 116 Use the graph for 5–6. Question 5. Mr. Torres took his students to the dolphin show. Each row in the stadium had 11 seats. One adult sat at each end of a row, and each group of 4 students was seated between 2 adults. Mr. Torres sat by himself. How many adults were there? _____ adults including Mr. Torres Answer: 13 adults. Explanation: First we must find total no. of rows, As there are 24 students each group contains 4 students, So 24 4= 6 rows. And one adult sat in each end of the row, So in 6 rows 2 people will sit. Therefore total adults are 6×2=12 adults+ Mr. Torres= 13 adults. Question 6. Another stadium section has 24 rows of 10 seats each. Describe at least two ways Mrs. Allen’s class can sit if an equal number of students sit in each row. Answer: 9 rows of 4 students or 6 rows of 6 students. Explanation: As there are 36 students in Mrs. Allen’s class. So students can sit in 6 rows of 6 students or 9 rows of 4 students. Question 7. Carol, Ann, and Liz each bought a toy fish. Carol’s fish is 10 inches longer than Ann’s fish. Liz’s fish is 2 inches longer than twice the length of Ann’s fish. Ann’s fish is 12 inches long. Find the length of each toy fish. Carol’s: _____ in. Liz’s: _____ in. Answer: Carol’s: 22 in., Liz’s: 26in. Explanation: Ann’s fish is 12 inches longer and Carol’s fish is 10 inches longer than Ann’s fish which means 10+12= 22 inches, So Carol’s fish is 22 inches. Liz’s fish is 2 inches longer than twice the length of Ann’s fish, which means (2×12) +2=24+2= 26 inches. Question 8. Evaluate Relationships Nell made a secret code. Each code word has 2 letters. Each word begins with a consonant and ends with a vowel. How many code words can Nell make with 3 consonants and 2 vowels? _____ code words Answer: 6 ways. Explanation: As each word begins with a consonant and ends with a vowel, So the first letter can be any one of 3 consonants and the second letter can be either one of 2 vowels. So Nell can make 3×2= 6 ways. Question 9. Allie is building a patio. The patio will have 8 tiles in each of 13 rows. She has already built the center section with 4 tiles in each of 7 rows. How many more tiles are needed to complete the patio? Show your work. Answer: 76 tiles. Explanation: Allie had 8 tiles in each of 13 rows, which means 13×8= 104 tiles. And the center section was built by 4 tiles in each of 7 rows, which means 4×7= 28 tiles. So 104-28= 76 tiles more needed to complete the patio. ### Common Core – Problem Solving Multistep Multiplication Problems – Page No. 117 Solve each problem. Question 1. A community park has 6 tables with a chessboard painted on top. Each board has 8 rows of 8 squares. When a game is set up, 4 rows of 8 squares on each board are covered with chess pieces. If a game is set up on each table, how many total squares are NOT covered by chess pieces? 4 × 8 = 32 32 × 6 = 192 squares Question 2. Jonah and his friends go apple picking. Jonah fills 5 baskets. Each basket holds 15 apples. If 4 of Jonah’s friends pick the same amount as Jonah, how many apples do Jonah and his friends pick in all? Draw a diagram to solve the problem. Answer: 375 apples. Explanation: As Jonah fills 5 baskets which holds 15 apples, So Jonah picked 15×5= 75 apples. And 4 of his friends pick same amount of apples, which means 75×4=300. So total apples Jonah and his friends picked up are 300+75= 375 apples. Question 3. There are 6 rows of 16 chairs set up for the third-grade play. In the first 4 rows, 2 chairs on each end are reserved for teachers. The rest of the chairs are for students. How many chairs are there for students? Answer: 80 chairs. Explanation: As there are 6 rows of 16 chairs which means 16×6= 96 total chairs. And first 4 rows 2 chairs on each end are reserved for teachers, which means 4×4= 16 chairs are reserved for teachers. So 96-16= 80 chairs are left for the students. ### Common Core – Problem Solving Multistep Multiplication Problems – Lesson Check – Page No. 118 Question 1. At a tree farm, there are 9 rows of 36 spruce trees. In each row, 14 of the spruce trees are blue spruce. How many spruce trees are NOT blue spruce? Options: a. 126 b. 198 c. 310 d. 324 Answer: b Explanation: There are 9 rows of 36 spruce trees which means 9×36= 324 spruce trees. And in that, each row has 14 blue spruce trees which mean 14×9= 126. So 324-126= 198 spruce trees are not blue. Question 2. Ron is tiling a countertop. He needs to place 54 square tiles in each of 8 rows to cover the counter. He wants to randomly place 8 groups of 4 blue tiles each and have the rest of the tiles be white. How many white tiles will Ron need? Options: a. 464 b. 432 c. 400 d. 32 Answer: c Explanation: Ron places 54 square tiles in each of 8 rows which means 54×8=432 tiles. And he randomly places 8 groups of 4 blue tiles which means 8×4= 32 blue tiles are placed. So no. of white tiles are 432-32= 400. Question 3. Juan reads a book with 368 pages. Savannah reads a book with 172 fewer pages than Juan’s book. How many pages are in the book Savannah reads? Options: a. 196 b. 216 c. 296 d. 540 Answer: a Explanation: Juan reads a book with 368 pages and Savannah reads a book with 172 fewer pages than Juan’s which means 368-172= 196 pages are in Savannah’s read. Question 4. Hailey has bottles that hold 678 pennies each. About how many pennies does she have if she has 6 bottles filled with pennies? Options: a. 3,600 b. 3,900 c. 4,200 d. 6,000 Answer: c Explanation: Let’s round off 678 to 700 and Hailey has bottles that hold 700 pennies each and if she has 6 bottles filled with pennies which means 700×6= 4200. Question 5. Terrence plants a garden that has 8 rows of flowers, with 28 flowers in each row. How many flowers did Terrence plant? Options: a. 1,664 b. 224 c. 164 d. 36 Answer: b Explanation: As the garden has 8 rows of flowers with 28 flowers in each row, So no. of flowers is 28×8= 224. Question 6. Kevin has 5 fish in his fish tank. Jasmine has 4 times as many fish as Kevin has. How many fish does Jasmine have? Options: a. 15 b. 20 c. 25 d. 30 Answer: b Explanation: As Kevin has 5 fishes and Jasmine has 4 times as many as Kevin which means 5×4= 20 fishes Jasmine has. ### Problem Solving Multistep Multiplication Problems – Page No. 121 Question 1. Use the model to find the product. 2 × 36 = _____ Answer: 72 Explanation: 2×36=2×(30+6) =(2×30)+(2×6) =60+12 =72 Estimate. Then record the product. Question 2. 4 2 × 4 —————- Estimate: _________ Product: _________ Answer: Estimate: 160 Product: 168 Explanation: Round off 42 to 40 and estimated value is 40×4= 160 and 42×4= 168 4 2 × 4 ——- 168 Question 3. 3 2 × 2 —————- Estimate: _________ Product: _________ Answer: Estimate: 60 Product: 64 Explanation: Round off 32 to 30 and the estimated value is 30×2= 60 and 32×2= 64. 3 2 × 2 —— 64 Question 4. 8 1 × 5 —————- Estimate: _________ Product: _________ Answer: Estimate: 400 Product: 405 Explanation: Round off 81 to 80 and the estimated value is 80×5= 400 and 81×5= 405. 81 × 5 —— 405 Question 5.$6 3
× 7
—————-
Estimate: $_________ Product:$ _________

Estimate: 420
Product: 441

Explanation: Round off 63 to 60 and the estimated value is 60×7= 420 and 63×7= 441.
$63 × 7 —— 441 Estimate. Then record the product. Question 8. 3 6 × 8 —————- Estimate: _________ Product: _________ Answer: Estimate: 320 Product: 288 Explanation: Round off 36 to 40 and the estimated value is 40×8= 320 and 36×8= 288. 36 × 8 —— 288 Question 9.$9 4
× 5
—————-
Estimate: $_________ Product:$ _________

Estimate: 450
Product: 470

Explanation: Round off 94 to 90 and the estimated value is 90×5= 450 and 94×5= 470.
$94 × 5 —— 470 Practice: Copy and Solve Estimate. Then record the product. Question 10. 3 × 82 Estimate: _________ Product: _________ Answer: Estimate: 240 Product: 246 Explanation: Round off 82 to 80 and the estimated value is 80×3= 240 and 82×3= 246. 3 2 × 2 —— 246 Question 11. 9 × 41 Estimate: _________ Product: _________ Answer: Estimate: 360 Product: 369 Explanation: Round off 41 to 40 and the estimated value is 40×9= 360 and 41×9= 369. 41 ×9 —— 369 Question 12. 7 ×$23
Estimate: $_________ Product:$ _________

Estimate: 140
Product: 161

Explanation: Round off 23 to 20 and the estimated value is 20×7= 140 and 23×7= 161.
23
× 7
——
161

Question 13.
8 × $54 Estimate:$ _________
Product: $_________ Answer: Estimate: 400 Product: 432 Explanation: Round off 54 to 50 and the estimated value is 50×8= 400 and 54×8= 432. 54 ×8 —— 432 Identify Relationships Algebra Write a rule. Find the unknown numbers. Question 15. Answer: 36, 60 Explanation: If 1 carton contains 12 eggs then 3 cartons will have 3×12= 36 and 5 cartons contains 5×12= 60. Question 16. Answer: 160, 192 Explanation: If 2 rows have 32 seats then 5 rows will have 5×32= 160 and 6 rows will have 6×32= 192 seats Question 17. It will cost$73 per hour to rent a sailboat and $88 per hour to rent a ski boat. How much more will it cost to rent a ski boat than a sailboat for 4 hours? Answer:$60.

Explanation: Cost of sailboat to rent per hour is $73 and for 4 hours it costs$73×4= $292. And cost of Ski boat to rent per hour is$88 and for 4 hours it costs $88×4=$352. So $352-$292= $60 much more costs for a ski boat than a sailboat.Problem Solving Multistep Multiplication Problems – Page No. 122 Use the table for 18–19. Question 18. At the speeds shown, how much farther could a black-tailed jackrabbit run than a desert cottontail in 7 seconds? Answer: 203 ft. Explanation: Black-tailed jackrabbit runs at a speed of 51 ft per sec, So in 7 seconds jackrabbit runs 51×7= 357 ft and Desert cottontail runs at a speed of 22 ft per sec, So in 7 seconds it runs 22×7= 154 ft. So 357-154= 203 ft could a black-tailed jackrabbit run than a desert cottontail in 7 seconds. Question 19. A black-tailed jackrabbit hops about 7 feet in a single hop. How far can it hop in 5 seconds? about ______ hops Answer: 35 hops. Explanation: As black-tailed jackrabbit hops about 7 feet in a single hop, So in 5 seconds it hops 7×5= 35. Question 21. The sum of two numbers is 31. The product of the two numbers is 150. What are the numbers? Answer: 6 and 25. Explanation: Let the numbers be X and Y, So the sum of two numbers is 31 which means X+Y=31 and the product of two numbers is 150 which means X×Y=150. So X=31-Y then replace X=31-Y, So (31-Y)×Y= 150, then 31Y-Y^2 = 150 which is Y^2 – 31Y+ 150 = 0. By factorization Y= 25 and X×25= 150 then X= 6. Therefore X= 6 and Y= 25. Question 23. Multiply 6 × 73. For 23a–23d, select True or False for each statement. a. A reasonable estimate of the product is$420.
i. True
ii. False

Explanation: 6×73= 438

Question 23.
b. Using partial products, the products are 42 and 180.
i. True
ii. False

Explanation: The partial products are 420 and 18

Question 23.
c. Using regrouping, 18 ones are regrouped as 8 tens and 1 one.
i. True
ii. False

Explanation: 8 tens and 1 one means 81.

Question 23.
d. The product is 438.
i. True
ii. False

Explanation: 6×73= 438

### Common Core – Multiply 2-Digit Numbers with Regrouping – Page No. 123

Estimate. Then record the product.

Question 1.
Estimate: 150

Question 2.
3 2
× 8
Estimate: ________
Product: ________

Estimate: 240
Product: 256

Explanation: Round off 32 to 30 and 30×8=240.
3 2
× 8
————
256

Estimate: 240
Product: 256

Explanation: Round off 32 to 30 and 30×8=240.
3 2
× 8
————
256

Estimate: 240
Product: 256

Explanation: Round off 32 to 30 and 30×8=240.
3 2
× 8
————
256

Question 3.
$5 5 × 2 Estimate:$ ________
Product: $________ Answer: Estimate:$120
Product: $110 Explanation: Round off 55 to 60 and 60×2= 120.$5 5
× 2
————-
$110 Question 4. 6 1 × 8 Estimate: ________ Product: ________ Answer: Estimate: 480 Product: 488 Explanation: Round off 61 to 60 and 60×8= 480. 6 1 × 8 ———– 488 Question 5. 3 7 × 9 Estimate: ________ Product: ________ Answer: Estimate: 360 Product: 333 Explanation: Round off 37 to 40 and 40×6= 360. 3 7 × 9 ———– 333 Question 6.$1 8
× 7
Estimate: $________ Product:$ ________

Estimate: $140 Product:$126

Explanation: Round off 18 to 20 and 20×7= 140.
$1 8 × 7 ———-$126

Question 7.
8 3
× 5
Estimate: ________
Product: ________

Estimate: 400
Product: 415

Explanation: Round off 83 to 80 and 80×5= 400.
8 3
× 5
——-
415

Question 8.
9 5
× 8
Estimate: ________
Product: ________

Estimate: 800
Product: 760

Explanation: Round off 95 to 100 and 100×8= 800.
9 5
× 8
——–
760

Question 9.
9 4
× 9
Estimate: ________
Product: ________

Estimate: 810
Product: 846

Explanation: Round off 94 to 90 and 90×9= 810.
9 4
× 9
——-
846

Question 10.
5 7
× 6
Estimate: ________
Product: ________

Estimate: 360
Product: 342

Explanation: Round off 57 to 60 and 60×6= 360.
5 7
× 6
——
342

Question 11.
7 2
× 3
Estimate: ________
Product: ________

Estimate: 210
Product: 216

Explanation: Round off 72 to 70 and 70×3= 210.
7 2
× 3
——-
216

Question 12.
$7 9 × 8 Estimate: ________ Product: ________ Answer: Estimate:$640
Product: $632 Explanation: Round off 79 to 80 and 80×8= 640.$7 9
× 8
——-
$632 Problem Solving Question 13. Sharon is 54 inches tall. A tree in her backyard is 5 times as tall as she is. The floor of her treehouse is at a height that is twice as tall as she is. What is the difference, in inches, between the top of the tree and the floor of the treehouse? Answer: 162 inches. Explanation: Sharon is 54 inches tall and a tree in her backyard is 5 times as tall as she is which means 54×5= 270. And her treehouse is twice as tall as she is which means 54×2= 108 inches. So the difference between the top of the tree and the floor of the treehouse is 270-108= 162 inches. Question 14. Mr. Diaz’s class is taking a field trip to the science museum. There are 23 students in the class, and a student admission ticket is$8. How much will the student
tickets cost?

Answer: $184. Explanation: Total no. of students are 23 and tickets cost is$8, So 23×8= $184. ### Common Core – Multiply 2-Digit Numbers with Regrouping – Lesson Check – Page No. 124 Question 1. A ferryboat makes four trips to an island each day. The ferry can hold 88 people. If the ferry is full on each trip, how many passengers are carried by ferry each day? Options: a. 176 b. 322 c. 332 d. 352 Answer: d Explanation: Total trips made by the ferryboat each day are 4 and it can hold 88 people, So 88×4= 352 passengers are carried by ferryboat each day. Question 2. Julian counted the number of times he drove across the Seven Mile Bridge while vacationing in the Florida Keys. He crossed the bridge 34 times. How many miles in all did Julian drive crossing the bridge? Options: a. 328 miles b. 248 miles c. 238 miles d. 218 miles Answer: c Explanation: No. of times Julian drive across the bridge is 7 miles and he crossed the bridge 34 times, So 34×7= 238 miles Julian drive crossing the bridge. Spiral Review Question 3. Sebastian wrote the population of his city as 300,000 + 40,000 + 60 + 7. Which of the following shows the population of Sebastian’s city written in standard form? Options: a. 346,700 b. 340,670 c. 340,607 d. 340,067 Answer: d Explanation: 300,000+40,000+60+7= 340,067. Question 4. A plane flew 2,190 kilometers from Chicago to Flagstaff. Another plane flew 2,910 kilometers from Chicago to Oakland. How much farther did the plane that flew to Oakland fly than the plane that flew to Flagstaff? Options: a. 720 kilometers b. 820 kilometers c. 5,000 kilometers d. 5,100 kilometers Answer: a Explanation: Plane flew from Chicago to Flagstaff is 2,190 km and another plane flew from Chicago to Oakland is 2,910, So 2910-2190= 720 km. Question 5. Tori buys 27 packages of miniature racing cars. Each package contains 5 cars. About how many miniature racing cars does Tori buy? Options: a. 15 b. 32 c. 100 d. 150 Answer: d Explanation: Let’s round off 27 packages to 30 and each package contains 5 cars, which means 30×5=150. Question 6. Which of the following equations represents the Distributive Property? Options: a. 3 × 4 = 4 × 3 b. 9 × 0 = 0 c. 5 × (3 + 4) = (5 × 3) + (5 × 4) d. 6 × (3 × 2) = (6 × 3) × 2 Answer: c Explanation: Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. ### Multiply 2-Digit Numbers with Regrouping – Page No. 127 Question 1. Tell what is happening in Step 1 of the problem. Answer: Multiplying 4×6 Explanation: In step 1 Multiplying 4×6= 24. Estimate. Then find the product. Question 2. 6 0 3 × 4 ———— 2,400 Estimate: __________ Product: ___________ Answer: Estimate: 2400 Product: 2412 Explanation: Rounding off 603 to 600 then 600×4= 2400. 6 0 3 × 4 ——– 2412 Question 3. 1,935 × 7 ———— Estimate: __________ Product: ___________ Answer: Estimate: 14,000. Product: 13,545. Explanation: Rounding off 1935 to 2000 then 2000×7= 14,000. 1,935 × 7 ——— 13,545 Question 4.$ 8,326
×       5
————
Estimate: $__________ Product:$ ___________

Estimate: 40,000
Product: 41,630

Explanation: Rounding off 8326 to 8000 then 8000×5= 40,000.
$8,326 × 5 ———- 41,630 Estimate. Then find the product. Question 7.$ 4,123
×       6
—————–
Estimate: $__________ Product:$ ___________

Estimate: 24,000.
Product: 24,738

Explanation: Rounding off 4,123 to 4000 then 4000×6= 24,000.
$4,123 × 6 ———– 24,738 Question 8. Mr. Jackson has$5,400 to buy supplies for the school computer lab. He buys 8 boxes of printer ink that cost $149 each and 3 printers that cost$1,017 each. How much money will Mr. Jackson have left after he buys the printer ink and printers?

Explanation: Airplane tickets cost for Alaska is $958 each. As Harrison family are 4 members so it will cost$958×4= $3,832 And for Vancouver it costs$734 each. So $734×4=$2,936 and Harrison family save $3832-$2936= $896. Question 16. Philadelphia, Pennsylvania, is 2,147 miles from Salt Lake City, Utah, and 2,868 miles from Portland, Oregon. What is the difference in the round-trip distances between Philadelphia and each of the other two cities? Explain whether you need an estimate or an exact answer. Answer: 1,442 mi. Explanation: The distance between Philadelphia and Salt Lake is 2,147 miles and the round-trip distance is 2×2,147= 4,294 miles. And the distance between Philadelphia and Portland is 2,868 miles and the round-trip distance is 2×2868= 5736 miles. So the difference is 5,736-4,294= 1442 miles. Question 17. Verify the Reasoning of Others Joe says that the product of a 4-digit number and a 1-digit number is always a 4-digit number. Does Joe’s statement make sense? Explain. Answer: No, Joe’s statement is incorrect. Explanation: As there are regrouped thousands, the product of a 4-digit number and a 1-digit number can have 5 digits. ### Common Core – Multiply 3-Digit and 4-Digit Numbers with Regrouping – Page No. 129 Estimate. Then find the product. Question 1. Estimate: 4,000 Question 2. 5,339 × 6 ————- Estimate: ________ Product: ________ Answer: Estimate: 30,000 Product: 32,034 Explanation: Round off 5,339 to 5000 then 5000×6= 30,000. 5,339 × 6 ———- 32,034 Question 3.$879
×   8
————-
Estimate: $________ Product:$ ________

Estimate: $7,200. Product:$7,032.

Explanation: Round off 879 to 900 then 900×8= 7,200.
$879 × 8 ——– 7,032 Question 4. 3,182 × 5 ————- Estimate: ________ Product: ________ Answer: Estimate: 15,000 Product: 15,910 Explanation: Round off 3,182 to 3000 then 3000×5= 15,000. 3,182 × 5 ———- 15,910 Question 5. 4,616 × 3 ————- Estimate: ________ Product: ________ Answer: Estimate: 15,000 Product: 13,848 Explanation: Round off 4,616 to 5,000 then 5000×3= 15,000. 4,616 × 3 ——— 13,848 Question 6. 2,854 × 9 ————- Estimate: ________ Product: ________ Answer: Estimate: 27,000 Product: 25,686 Explanation: Round off 2,854 to 3000 then 3000×9= 27,000. 2,854 × 9 ——— 25,686 Question 7. 7,500 × 2 ————- Estimate: ________ Product: ________ Answer: Estimate: 16,000 Product: 15,000 Explanation: Round off 7,500 to 8000 then 8000×2= 16,000. 7,500 × 2 ——— 15,000 Question 8. 9 4 8 × 7 ————- Estimate: ________ Product: ________ Answer: Estimate: 6,300 Product: 6,636 Explanation: Explanation: Round off 948 to 900 then 900×7= 6,300. 9 4 8 × 7 ——- 6,636 Question 9. 1,752 × 6 ————- Estimate: ________ Product: ________ Answer: Estimate: 12,000. Product: 10,512. Explanation: Explanation: Round off 1,752 to 2000 then 2000×6= 12,000. 1,752 × 6 ———– 10,512 Question 10. 5 5 0 × 9 ————- Estimate: ________ Product: ________ Answer: Estimate: 5,400 Product: 4,950 Explanation: Round off 550 to 600 then 600×9= 5,400. 5 5 0 × 9 ——– 4,950 Question 11. 6,839 × 4 ————- Estimate: ________ Product: ________ Answer: Estimate: 28,000 Product: 27,356 Explanation: Round off 6,839 to 7000 then 7000×4= 28,000. 6,839 × 4 ———- 27,356 Question 12.$9,614
×      6
————-
Estimate: $________ Product:$ ________

Estimate: 60,000.
Product: 57,684.

Explanation: Round off 9,614 to 10,000 then 10,000×6= 60,000.
$9,614 × 6 ———- 57,684 Problem Solving Question 13. Lafayette County has a population of 7,022 people. Columbia County’s population is 8 times as great as Lafayette County’s population. What is the population of Columbia County? Answer: 56,176 people Explanation: Lafayette County has a population of 7,022 people and Columbia County’s population is 8 times Lafayette County which means 7,022×8= 56,176. Question 14. A seafood company sold 9,125 pounds of fish last month. If 6 seafood companies sold the same amount of fish, how much fish did the 6 companies sell last month in all? Answer: 54,750 pounds. Explanation: As the seafood company sold 9,125 pounds of fishes last month and 6 seafood companies also sold the same amount which means 9,125×6= 54,750 pounds. ### Common Core – Multiply 3-Digit and 4-Digit Numbers with Regrouping – Lesson Check – Page No. 130 Question 1. By recycling 1 ton of paper, 6,953 gallons of water are saved. How many gallons of water are saved by recycling 4 tons of paper? Options: a. 24,602 gallons b. 27,612 gallons c. 27,812 gallons d. 28,000 gallons Answer: c Explanation: As 1 ton of paper saves 6,953 gallons of water, So 4 tons of paper can save 6,953×4= 27,812. Question 2. Esteban counted the number of steps it took him to walk to school. He counted 1,138 steps. How many steps does he take walking to and from school each day? Options: a. 2,000 b. 2,266 c. 2,276 d. 22,616 Answer: c Explanation: As Esteban counted 1,138 steps to school and from school, it will be 1,138+1,138=2,276 steps Spiral Review Question 3. A website has 13,406 people registered. What is the word form of this number? Options: a. thirty thousand, four hundred six b. thirteen thousand, four hundred sixty c. thirteen thousand, four hundred six d. thirteen thousand, six hundred six Answer: c Explanation: 13,406 in words are thirteen thousand four hundred six. Question 4. In one year, the McAlister family drove their car 15,680 miles. To the nearest thousand, how many miles did they drive their car that year? Options: a. 15,000 miles b. 15,700 miles c. 16,000 miles d. 20,000 miles Answer: c Explanation: 15,680 nearest thousand is 16,000 Question 5. Connor scored 14,370 points in a game. Amy scored 1,089 fewer points than Connor. How many points did Amy score? Options: a. 12,281 b. 13,281 c. 15,359 d. 15,459 Answer: b Explanation: Connor scored 14,370 points and Amy scored 1,089 fewer points, So Amy score is 14,370-1089= 13,281. Question 6. Lea buys 6 model cars that each cost$15. She also buys 4 bottles of paint that each cost $11. How much does Lea spend in all on model cars and paint? Options: a.$134
b. $90 c.$44
d. $36 Answer: a Explanation: Lea buys 6 model cars that each cost$15, So the total cost for cars is $15×6=$90.
And 4 bottles of paint that each cost $11, So the total cost of paints is$11×4= $44. Then$90+$44=$134.

### Multiply 3-Digit and 4-Digit Numbers with Regrouping – Page No. 133

Question 1.
Use the order of operations to find the value of n.
5 × 17 + 5 × 20 – 32 = n
n = ______

Explanation: (5×17)+5×20 –32=
= 85+100-32
=185-32
=153

Find the value of n.

Question 4.
2 × 62 + 8 × 22 – 53 = n
n = ______

Explanation: 2×62+8×22–53=
= 124+176-53
=300-53
=247.

Question 5.
6 × 13 + 9 × 34 – 22 = n
n = ______

Explanation: 6×13+9×34–22=
=78+306-22
=384-22
=362.

Find the value of n.

Question 6.
8 × 42 + 3 × 59 – 62 = n
n = ______

Explanation: 8×42+3×59–62=
=336+177-62
=513-62
=451.

Question 7.
6 × 27 + 2 × 47 – 83 = n
n = ______

Explanation: 6×27+2×47–83=
=162+94-83
=256-83
=173

Question 8.
Maggie has 3 binders with 25 stamps in each binder. She has 5 binders with 24 baseball cards in each binder. If she gives 35 stamps to a friend, how many stamps and cards does she have left?

Explanation: Maggie has 3 binders with 25 stamps each binder, so total stamps are 3×25= 75. And 5 binders with 24 baseball cards in each binder. So total baseball cards are 24×5=120.
As she gave 35 stamps to a friend, so 75-35= 40. Total stamps and cards she has
120+40= 160

Question 9.
Evaluate Maddox has 4 boxes with 32 marbles in each box. He has 7 boxes with 18 shells in each box. If he gets 20 marbles from a friend, how many marbles and shells does he have?

Explanation: Maddox has 4 boxes and 32 marbles in each box, so 4×32= 128. And 7 boxes with 18 shells in each box which means 7×18= 126. And he got 20 marbles from a friend, so
128+20= 148 marbles. So total marbles and shells he has 148+126= 274.

Question 10.
The soccer team sells 54 bagels with cream cheese for $2 each and 36 muffins for$1 each during a bake sale. The coach uses the money to buy socks for the 14 players. The socks cost $6 per pair. How much money does the coach have left? Explain how you found your answer. Answer:$60.

Explanation: Soccer team sells 54 bagels with cream cheese for $2 each, so 54×2=$108 total amount raised by selling bagels with cream cheese. And 36 muffins for $1 each which means 36×$1= $36 raised by selling muffins. So the total amount raised is$108+$36=$144. And he uses the money to buy socks for 14 players and each pair is $6, So 14×$6= $84 needed to buy socks for the players. So$144-$84=$60 left with the coach after buying socks for the players.

### Multiply 3-Digit and 4-Digit Numbers with Regrouping – Page No. 134

Question 11.
What’s the Error? Dominic has 5 books with 12 postcards in each book. He has 4 boxes with 20 coins in each box. If he gives 15 post cards to a friend, how many postcards and coins does he have?

Dominic drew this model.

Dominic used these steps to solve.
5 × 12 + 4 × 20 – 15 = n
60 + 4 × 20 – 15 = n
64 × 20 – 15 = n
1,280 – 15 = n
1,265 = n
Look at the steps Dominic used to solve this problem. Find and describe his error.

Question 11.
Use the correct steps to solve the problem.

5 × 12 + 4 × 20 – 15 = n
60+4×20-15=n
60+80-15=n
140-15=n
125=n

### Common Core – Solve Multistep Problems Using Equations – Page No. 135

Find the value of n.

Question 1.
4 × 27 + 5 × 34 – 94 = n
108 + 5 × 34 – 94 = n
108 + 170 – 94 = n
278 – 94 = n
184 = n

Question 2.
7 × 38 + 3 × 45 – 56 = n
_____ = n

Explanation: 7×38+3×45-56=
=266+135-56
=401-56
=345

Question 3.
6 × 21 + 7 × 29 – 83 = n
_____ = n

Explanation: 6×21+7×29-83=
=126+203-83
=329-83
=246

Question 4.
9 × 19 + 2 × 57 – 75 = n
_____ = n

Explanation: 9×19+2×57-75=
=171+114-75
=285-75
=210.

Problem Solving

Question 7.
A bakery has 4 trays with 16 muffins on each tray. The bakery has 3 trays of cupcakes with 24 cupcakes on each tray. If 15 cupcakes are sold, how many muffins and cupcakes are left?

Explanation: 4×16+3×24-15=n
64+3×24-15=n
64+72-15=n
136-15=n
121=n

### Common Core – Solve Multistep Problems Using Equations – Lesson Check – Page No. 136

Question 1.
What is the value of n?
9 × 23 + 3 × 39 – 28 = n
Options:
a. 240
b. 296
c. 2,310
d. 8,162

Explanation: 9×23+3×39–28=
=207+117-28
=324-28
=296

Question 2.
Which expression has a value of 199?
Options:
a. 4 × 28 + 6 × 17 – 15
b. 4 × 17 + 6 × 28 – 38
c. 4 × 38 + 6 × 15 – 28
d. 4 × 15 + 6 × 38 – 88

Explanation: 4×28+6×17-15=
=112+102-15
=214-15
=199.

Spiral Review

Question 3.
Which expression shows how you can multiply 9 × 475 using expanded form and the Distributive Property?
Options:
a. (9 × 4) + (9 × 7) + (9 × 5)
b. (9 × 4) + (9 × 70) + (9 × 700)
c. (9 × 400) + (9 × 70) + (9 × 5)
d. (9 × 400) + (9 × 700) + (9 × 500)

Explanation: Distributive property means if we multiplying a sum by a number is the same as multiplying each addend by the number and adding the products.
9 × 475= (9×400)+(9×70)+(9×5)

Question 4.
Which equation best represents the comparison sentence?
32 is 8 times as many as 4
Options:
a. 32 = 8 × 4
b. 32 × 8 = 4
c. 32 = 8 + 4
d. 8 + 4 = 32

Explanation: 32=8×4

Question 5.
Between which pair of numbers is the exact product of 379 and 8?
Options:
a. between 2,400 and 2,500
b. between 2,400 and 2,800
c. between 2,400 and 3,000
d. between 2,400 and 3,200

Explanation: 379×8= 3,032

Question 6.
Which of the following statements shows the halving and doubling strategy to find 28 × 50?
Options:
a. 28 × 50 = 14 × 100
b. 28 × 50 = (14 × 25) × (14 × 25)
c. 28 × 50 = (20 × 50) × (8 × 50)
d. 28 × 50 = 2 × (14 × 25)

Explanation: 28×50 = 14×100

### Review/Test – Page No. 137

For 1–3, use the table.

Question 1.
What is the cost of 3 Bur Oak trees? Show your work.

Answer: $96. Explanation: Each Bur oak tree costs$32 for 3 and above, so $32×3=$96.

Question 2.
Mr. Tan buys 4 White Pine trees and 5 Birch trees. What is the cost of the trees? Show your work and explain how you found the answer.

Answer: $188. Explanation: As 4 white pine trees cost is$37 each, so $37×4=$148 and 5 birch trees cost $8 each, so 5×$8= $40. Total cost of trees are$148+$40=$188.

Question 3.
Rudy will buy 3 Ivory Silk Lilac trees or 2 Bur Oak trees. He wants to buy trees that cost less. What trees will he buy? How much will he save? Show your work.

Answer: Rudy will take 3 Ivory Silk Lilac trees which costs $66. Explanation: If Rudy buys 3 Ivory Silk Lilac trees which costs$22 each, so $22×3=$66. And if 2 Bur Oak trees price is $35 each it means$35×2= $70. As Rudy wants to buy the trees that cost less, so he will take 3 Ivory Silk Lilac trees which cost$66.

### Review/Test – Page No. 138

Question 4.
For numbers 4a–4d, select True or False for each equation.
a. 7 × 194 = 1,338
i. True
ii. False

Explanation: 7×194= 1,338.

Question 4.
b. 5 × 5,126 = 25,630
i. True
ii. False

Explanation: 5×5,126= 25,630.

Question 4.
c. 8 × 367 = 2,926
i. True
ii. False

Explanation: 8×367= 2,936

Question 4.
d. 4 × 3,952 = 15,808
i. True
ii. False

Explanation: 4×3952= 15,808

Question 5.
Part A
Draw a line to match each section in the model to the partial product it represents.

Question 5.
Part B
Then find 3 × 146. Show your work and explain.

Explanation: By distributive property
3×146= 3×(100+40+6)
=(3×100)+(3×40)+( 3×6)
=300+120+18
=438.

### Review/Test – Page No. 139

Question 6.
For numbers 6a–6c, write an equation or a comparison sentence using the numbers on the tiles.
a.

______ times as many as ______ is ______ .

Answer: 8 times as many as 4 is 32.

Explanation: 8×4= 32.

Question 6.
b.

______ × ______ = ______

Answer: 6 times as many as 8 is 48.

Explanation: 6×8= 48.

Question 6.
c.
9 × 3 = 27
______ times as many as ______ is ______ .

Answer: 9 times as many as 3 is 27

Question 7.
Multiply 7 × 43. For 7a–7d, select True or False for each statement.
a. A reasonable estimate of the product is 280.
i. True
ii. False

Explanation: 7×43= 301. Take 43 and round off to 40 then 40×7= 280.

Question 7.
b. Using partial products, the products are 21 and 28.
i. True
ii. False

Explanation: 7×43= 7×(40+3)
=(7×40)+(7×3)
=280+21. So partial products are 280 and 21.

Question 7.
c. Using regrouping, 21 ones are regrouped as 1 ten and 2 ones.
i. True
ii. False

Explanation: 1 ten and 2 ones is 12

Question 7.
d. The product is 301.
i. True
ii. False

Explanation: 7×43= 7×(40+3)
=(7×40)+(7×3)
=280+21
=301.

### Review/Test – Page No. 140

Question 9.
Multiply 7 × 462 using place value and expanded form.
Choose the number from the box to complete the expression.

Explanation: 7×462= 7×(400+60+2).

Question 10.
For numbers 10a–10b, use place value to find the product.
a.
3 × 600 = 3 × ______ hundreds
= ______ hundreds
______

Answer: 6 hundreds, 18 hundreds , 1800

Explanation: 3 × 600 = 3 × 6 hundreds
= 18 hundreds
= 1800.

Question 10.
b.
5 × 400 = 5 × ______ hundreds
______ hundreds
______

Explanation: 5 × 400 = 5 × 4hundreds
= 20 hundreds
= 2,000.

Question 11.
Liam has 3 boxes of baseball cards with 50 cards in each box. He also has 5 boxes with 40 basketball cards in each box. If Liam goes to the store and buys 50 more baseball cards, how many baseball and basketball cards does Liam have? Show your work.

Answer: Liam has 400 baseball and baseball cards.

Explanation: Liam has 3 boxes of baseball cards and there are 50 cards in each box, so total cards are 50×3= 150 baseball cards. And he has 5 boxes with 40 baseball cards in each box which means 5×40= 200. So total baseball cards are 150+200= 350. And he went to the store to buy 50 more baseball cards, so total baseball cards are 350+50= 400.

### Review/Test – Page No. 141

Question 12.
There is a book sale at the library. The price for each book is $4. Which expression can be used to show how much money the library will make if it sells 289 books? Use the numbers on the tiles to complete your answer. (4 × ______) + (4 × ______) + (4 × ______) Answer: 200, 80, 9. Explanation: As the price of each book is$4, so for 289 books it will be 4×289
= 4×(200+80+9)
=(4×200)+(4×80)+(4×9)
=800+320+36
=1,156.

Question 14.
A clown bought 6 bags of round balloons with 24 balloons in each bag. The clown also bought 3 bags of long balloons with 36 balloons in each bag.
Part A
How many more long balloons than round balloons did the clown buy? Show your work.
______ balloons

Explanation: As clown bought 6 bags of round balloons with 24 balloons in each bag, so
6×24= 144 and 3 bags of long balloons with 36 balloons in each bag, so 3×36= 108, So
144-108= 36.

Question 14.
Part B
The clown also bought 5 bags of heart-shaped balloons with 14 balloons in each bag. When the clown blew up all of the round, long, and heart-shaped balloons, 23 balloons burst. How many blown-up balloons were left? Explain your answer.
______ blown-up balloons

Explanation: The no. of heart-shaped balloons is 5×14= 70. Then add that number to the number of round balloons and long balloons 70+144+108= 322 balloons in all. Then subtract the number of burst balloons, so 322-23= 299 balloons left.

### Review/Test – Page No. 142

Question 15.
Hector planted 185 flowers in 2 days. There were 5 volunteers, including Hector, who each planted about the same number of flowers. About how many flowers did they plant?

Explanation: Hector planted 185 flowers in 2 days, so 5 volunteers can plant 185×5= 925.

Question 16.
Jay and Blair went fishing. Together, they caught 27 fish. Jay caught 2 times as many fish as Blair. How many fish did Jay and Blair each catch? Write an equation and solve. Explain your work.
Jay: ______ fish;         Blair: ______ fish

Answer: Blair caught 9 fishes and Jay caught 18 fishes.

Explanation: Blair caught n fish and Jay caught 2×n fish. Together they caught 3×n fish, so
3×n= 27 and n= 9 fishes, and 2×n= 18 fishes. Blair caught 9 fishes and Jay caught 18 fishes

Question 17.
At the pet fair, Darlene’s dog weighed 5 times as much as Leah’s dog. Together, the dogs weighed 84 pounds. How much did each dog weigh? Complete the bar model. Write an equation and solve.

Leah’s dog: ______ pounds; Darlene’s dog: ______ pounds;

Answer: Leah’s dog is 14 pound and Darlene’s dog weight is 70 pounds.

Explanation:

Let Leah’s dog weight be X and Darlene’s is 5 times as many as Leah’s, so Darlene’s dog weight be 5X. As together weight is 84 pounds, then X+5X= 84 and X= 14. So Leah’s dog weight is 14 and Darlene’s dog weight is 5×14= 70.

Question 18.
Use the Distributive Property to model the product on the grid.
Record the product.

4 × 12 = ______

Explanation: 4×12=4×(10+2)
=(4×10)+(4×2)
=40+8
=48

### Page No. 147

Question 1.
Find 20 × 27. Tell which method you chose. Explain what happens in each step.

Explanation: It is mental maths. Because 2×27= 54 and 20×27= 540.

Choose a method. Then find the product.

Question 4.
40 × 24 = ______

Explanation: Mental math, as 4×24=96 and 40×24= 960

Question 5.
11 × 60 = ______

Explanation: Mental math, as 11×6=66 and 11×60= 660

Choose a method. Then find the product.

Question 6.
70 × 55 = ______

Explanation: Mental math, as 7×55=385 and 70×55= 3850

Question 7.
17 × 30 = ______

Explanation: Mental math, as 17×3=51 and 17×30= 510

Question 8.
30 × 60 = ______

Explanation: Mental math, as 30×60=1800 and 30×60= 1800

Question 9.
12 × 90 = ______

Explanation: Mental math, as 12×9=108 and 12×90= 1080.

Reason Quantitatively Algebra Find the unknown digit in the number.

Question 10.
64 × 40 = 2,56■
■ = ______

Explanation: Mental math, as 64×4=256 and 64×40= 510

Question 11.
29× 50 = 1,★50
★ = ______

Explanation: Mental math, as 29×5=145 and 29×50= 1450

Question 12.
3⧫× 47 = 1,410
⧫ = ______

Explanation: Mental math, as 3×47=1410 and 30×47= 1410

Question 13.
Caroline packs 12 jars of jam in a box. She has 40 boxes. She has 542 jars of jam. How many jars of jam will she have left when all the boxes are full?

Explanation: Caroline packs 12 jars in a box and she has 40 boxes, so total boxes are
12×40= 480 boxes. As she has 542 jars of jam, so total jars left are 542-480= 62 jars.

Question 14.
Alison is preparing for a math contest. Each day, she works on multiplication problems for 20 minutes and division problems for 10 minutes. How many minutes does Alison practice multiplication and division problems in 15 days?

Explanation: As Alison works on multiplication problems for 20 mins and 10 mins on division problems, So total time taken by Alison is 20+10=30 mins. So for 15 days Alison takes
15×30= 450 mins.

### Page No. 148

Use the table for 15–16.

Question 15.
Use Graphs How many frames did it take to produce 50 seconds of Pinocchio?

Explanation: Total frames are 50×19= 950 frames.

Question 16.
Are there fewer frames in 10 seconds of The Flintstones or in 14 seconds of The Enchanted Drawing? What is the difference in the number of frames?

Explanation: The Flintstone frames in 10 seconds are 10×24= 240 and The Enchanted Drawing frames are 14×20= 280. So the difference between them is 280-240= 40.

Question 17.
The product of my number and twice my number is 128. What is half my number? Explain how you solved the problem.

Explanation: First make a table to test numbers less than 10 since 10×20= 200, and 2×8= 16 then 8×16= 128 and 8÷2= 4.

Question 18.
Tanya says that the product of a multiple of ten and a multiple of ten will always have only one zero. Is she correct? Explain.

Explanation: The product of two multiples of ten will always have at least 2 zeros.

Question 19.
For numbers 19a–19e, select Yes or No to tell whether the answer is correct.
a. 28 × 10 = 280
i. yes
ii. no

Question 19.
b. 15 × 20 = 300
i. yes
ii. no

Question 19.
c. 17 × 10 = 17
i. yes
ii. no

Question 19.
d. 80 × 10 = 800
i. yes
ii. no

Question 19.
e. 16 × 30 = 1,800
i. yes
ii. no

## Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million

### Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million

Chapter 1 of Go Math 4th Grade Answer Keys includes topis like Place value relationships, Read and write numbers, Compare and Order numbers, Round numbers, Rename numbers, etc. All these topics are illustrated explicitly which addresses the toppers to learn quickly. Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million Questions & Solutions are provided in a fundamental way that makes students not find any difficulty in learning & solving.
Chapter 1-Lesson 1:

Chapter 1-Lesson 2:

Chapter 1-Lesson 3:

Chapter 1-Lesson 4:

Chapter 1-Lesson 5:

Chapter 1-Lesson 6:

Chapter 1-Lesson 7:

Chapter 1-Lesson 8:

Chapter 1-Lesson 9:

### Common Core – Model Place Value Relationships (Page 5)

Question 1.
Describe the pattern in the shapes of the models. What will be the shape of the model for 10,000?

Answer: The pattern shows cube, long, flat, cube. So the shape of the model for 10,000 will be long.

Question 2.
Describe the pattern you see in the sizes of the models. How will the size of the model for 100,000 compare to the size of the model for 10,000?

Answer: Each model is 10 times the previous model, so the model for 100,000 will be 10 times the size of the model for 10,000.

### Common Core – Model Place Value Relationships (Page 6)

Value of a Digit

The value of a digit depends on its place-value position in the number. A place-value chart can help you understand the value of each digit in a number. The value of each place is 10 times the value of the place to the right.

Question 1.
The value of the digit 9 is 9 ten thousands, or:

Answer: The place value of the digit 9 in 894,613 is 90,000.

Explanation: Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 9 in 8,94,613 is 90,000.

Compare the values of the underlined digits.
2,304 16,135

Answer: The value of 3 in 2,304 is 10 times the value of 3 in 16,135.

Explanation: Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 3 in 2,304 is 300. And the place value of the digit 3 in 16,135 is 30. As each hundred is 10 times as many as 10, so 3 hundreds are ten times as many as 3 tens. So, the value of 3 in 2,304 is 10 times the value of 3 in 16,135.

Question 2.
STEP 1 Find the value of 3 in 2,304.
Show 2,304 in a place-value chart.

Answer: The value of 3 in 2,304 is 300

Explanation:

Question 2.
STEP 2 Find the value of 3 in 16,135.

Show 16,135 in a place-value chart.

So, the value of 3 in 2,304 is ___________ times the value of 3 in 16,135.

Answer: The value of 3 in 16,135 is 30. So, the value of 3 in 2,304 is 10 times the value of 3 in 16,135.

Explanation:
Each hundred is 10 times as many as 10, so 3 hundreds are ten times as many as 3 tens. So, the value of 3 in 16,135 is 30. So, the value of 3 in 2,304 is 10 times the value of 3 in 16,135.

### Common Core – Model Place Value Relationships (Page 7)

Question 1.
Complete the table below.

Explanation:

Find the value of the underlined digit.

Question 2.
703,890

Answer: The value of the digit 7 in 703,890 is 700,000.

Explanation: Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 7 in 703,890 is 700,000.

Question 3.
63,540

Answer: The value of the digit 4 in 63,540 is 40.

Explanation: Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 4 in 63,540 is 40.

Compare the values of the underlined digits.

Question 6.
2,000 and 200

The value of 2 in 2,000 is ___________ times the value of 2 in 200

Explanation: The value of 2 in 2000 is 10 times the value of 2 in 200.

Question 7.
40 and 400

The value of 4 in 400 is ___________ times the value of 4 in 40

Explanation: The value of 4 in 400 is 10 times the value of 4 in 40.

Find the value of the underlined digit.

Question 8.
230,001

Answer: The place value of the digit 3 in 230,001 is 30,000.

Explanation: Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 3 in 230,001 is 30,000.

Question 9.
803,040

Answer: The place value of the digit 3 in 230,001 is 30,000.

Explanation: Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 3 in 230,001 is 30,000.

Question 10.
46,842

Answer: The place value of the digit 2 in 46,842 is 2.

Explanation: Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 2 in 46,842 is 2.

Question 11.
980,650

Answer: The place value of the digit 9 in 980,650 is 900,000.

Explanation: Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 9 in 980,650 is 900,000.

Compare the values of the underlined digits.

Question 14.
Greg has collected 4,385 pennies and Hannah has collected 3,899 pennies. How many times as great as the value of 3 in 4,385 is the value of 3 in 3,899?

Answer: The value of the digit 3 in 3,899 is 10 times more than the value of the digit 3 in 4,385.

Explanation:
The value of the digit 3 is 4,385 is 300 and the value of 3 in 3,899 is 3000. So the value of the digit 3 in 3,899 is 10 times more than the value of the digit 3 in 4,385.

Question 15.
Shawn wants to model the number 13,450 using base-ten blocks. How many large cubes, flats, and longs does he need to model the number?

Answer: Shawn needs 13 large cubes, 4 flats, and 5 longs.

Explanation: Each large cube represents 1000, so 13 large cubes will represent 13×1000= 13,000, and each flat represents 100 so every 4 flats represent 4×100= 400, and each long represents 10 so 5 longs represent 5×10= 50.
So 13,000+400+50= 13,450.

### Common Core – Model Place Value Relationships (Page 8)

Question 14.
What is the value of digit 7 in the population of Memphis?

Answer: The value of digit 7 in 676,640 is 70,000.

Explanation: The population of Memphis is 676,640, so the value of digit 7 in 676,640 is 70,000.

Question 14.
What is the value of digit 1 in the population of Denver?

Answer: The value of the digit 1in 610,345 is 10,000.

Explanation: The population of Denver is 610,345, so the value of the digit 1in 610,345 is 10,000.

Question 14.
How many times as great as the value of the digit 1 in the population of Cleveland is this value?

Answer: The value of digit 1 in 431,369 is 1000.

Explanation: The population of Cleveland is 431,369, so the value of digit 1 in 431,369 is 1000.

Question 14.
Which city’s population has a 4 in the hundred thousands place?

Answer: Cleveland is the city with 4 in the hundred thousands place.

Explanation: Cleveland is the city with 4 in the hundred thousands place. As the population of Cleveland is 431,369 and the value of 4 in 431,369 is 400,000.

Question 15.
How many models of 100 do you need to model 3,200? Explain.

Explanation: As 3 thousands are the same as 30 hundreds, so 30 hundreds+ 2 hundreds= 32 hundreds.

Question 17.
There are 686,147 books at the Greenville Library. What is the value of the digit 8 in this number?
(a) 80
(b) 8,000
(c) 80,000
(d) 800.000

Answer: The value of the digit 8 in 686,147 is 80,000.

Explanation: As there are 686,147 books in the library, so the value of the digit 8 in 686,147 is 80,000.

Question 18.
The value of 7 in 375,081 is 7,000.
(a) True
(b) False

Explanation: As the digit 7 is in thousands place, so the value of 7 in 375,081 is 70,000.

Question 18.
The value of 6 in 269,480 is 600,000.
(a) True
(b) False

Explanation: As the digit 6 is in thousands’ place, so the value of 6 in 269,480 is 60,000.

Question 18.
The value of 5 in 427,593 is 500.
(a) True
(b) False

Explanation: As the digit 5 is in the hundreds place, so the value of 5 in 427,593 is 500.

Question 18.
The value of 1 in 375,081 is 10.
(a) True
(b) False

Explanation: As the digit 1 is in ones place, so the value of 1 in 375,081 is 1.

Question 18.
The value of 4 in 943,268 is 40,000.
(a) True
(b) False

Explanation: As the digit 4 is in thousands place, so the value of 4 in 943,268 is 40,000.

### Model Place Value Relationships

Find the value of the underlined digit.

Question 1.
6,035
30

Question 2.
43,782

Answer: The value of 7 in 43,782 is 700

Explanation: As the digit 7 is in hundreds place so the value of 7 in 43,782 is 700.

Question 3.
506,087

Answer: The value of 7 in 506,087 is 7.

Explanation: As the digit 7 is in ones place so the value of 7 in 506,087 is 7.

Question 4.
49,254

Answer: The value of 9 in 49,254 is 9,000.

Explanation: As the digit 9 is in thousands place so the value of 9 in 49,254 is 9,000.

Question 8.
736,144

Answer: The value of 6 in 736,144 is 6,000.

Explanation: As the digit 6 is in thousands place so the value of 6 in 736,144 is 6,000.

Compare the values of the underlined digits.

Question 9.
6,300 and 530

The value of 3 in ___________ is ___________ times the value of 3 in ___________ .

Answer: The value of 3 in 6,300 is 10 times the value of 3 in 530.

Explanation:
The value of 3 in 6300 is 300 and the value of 3 in 530 is 30.
So the value of 3 in 6,300 is 10 times the value of 3 in 530.

Question 10.
2,783 and 7,283

The value of 2 in ___________ is ___________ times the value of 2 in ___________ .

Answer: The value of 2 in 2,738 is 10 times the value of 2 in 7,238.

Explanation:
The value of 2 in 2,738 is 2,000 and the value of 2 in 7,238 is 200.
So the value of 2 in 2,738 is 10 times the value of 2 in 7,238.

Question 12.
503,497 and 26,475

The value of 7 in ___________ is ___________ times the value of 7 in ___________.

Answer: The value of 7 in 26,475 is 10 times the value of 7 in 503,497.

Explanation:
The value of 7 in 26,475 is 70 and the value of 7 in 503,497 is 7.
So the value of 7 in 26,475 is 10 times the value of 7 in 503,497.

Problem Solving

Use the table for 13–14.

Question 13.
What is the value of the digit 9 in the attendance at the Redskins vs. Titans game?

The value of 9 is ___________ .

Answer: The value of 9 is 9,000.

Explanation: As the digit 9 is in thousands place, so the value of the digit 9 in 69,143 is 9,000.

Question 14.
The attendance at which game has a 7 in the ten thousands place?

Answer: Ravens vs. Panthers attendance is 73,021

Explanation: The attendance at Ravens vs. Panthers game has a 7 in the ten thousands place.

### Common Core – Model Place Value Relationships (Page 10)

Lesson Check

Question 1.
During one season, a total of 453,193 people attended a baseball team’s games. What is the value of the digit 5 in the number of people?
(a) 500
(b) 5,000
(c) 50,000
(d) 500,000

Explanation: The total number of people attended for baseball game are 453,193 and the value of the digit 5 in 453,193 is 5 ten thousands which is 50,000.

Question 2.
Hal forgot the number of people at the basketball game. He does remember that the number had a 3 in the tens place. Which number could Hal be thinking of?
(a) 7,321
(b) 3,172
(c) 2,713
(d) 1,237

Explanation: The number which has 3 in tens place is 1,237.

Spiral Review

Question 3.
Hot dog buns come in packages of 8. For the school picnic, Mr. Spencer bought 30 packages of hot dog buns. How many hot dog buns did he buy?
(a) 24
(b) 38
(c) 110
(d) 240

Explanation: The number of hot dog buns in a package are 8 and Mr. Spencer bought 30 packages, so the total number of hot dog buns he bought is 8×30= 240.

Question 4.
There are 8 students on the minibus. Five of the students are boys. What fraction of the students are boys?
(a) $$\frac{3}{8}$$
(b) $$\frac{5}{8}$$
(c) $$\frac{5}{5}$$
(d) $$\frac{8}{8}$$

Explanation: The total number of students are 8 and in that 5 are boys, so the fraction of the students are boys is $$\frac{5}{8}$$

Question 5.
The clock below shows the time when Amber leaves home for school. At what time does Amber leave home?

(a) 2:41
(b) 8:02
(c) 8:10
(d) 8:20