HMH Go Math

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

• Equivalent Fractions – Page No. 331
• Equivalent Fractions Lesson Check – Page No. 332

Lesson 2: Generate Equivalent Fractions

• Generate Equivalent Fractions – Page No. 335
• Generate Equivalent Fractions Lesson Check – Page No. 336
• Generate Equivalent Fractions Lesson Check 1 – Page No. 337
• Generate Equivalent Fractions Lesson Check 2 – Page No. 338

Lesson 3: Simplest Form

• Simplest Form – Page No. 341
• Simplest Form Lesson Check – Page No. 342
• Simplest Form Lesson Check 1 – Page No. 343
• Simplest Form Lesson Check 2 – Page No. 344

Lesson 4: Common Denominators

• Common Denominators – Page No. 347
• Common Denominators Lesson Check – Page No. 348
• Common Denominators Lesson Check 1 – Page No. 349
• Common Denominators Lesson Check 2 – Page No. 350
• Common Denominators Lesson Check 3 – Page No. 353
• Common Denominators Lesson Check 4 – Page No. 354

Lesson 5: Problem Solving • Find Equivalent Fractions

• Find Equivalent Fractions – Page No. 355
• Find Equivalent Fractions Lesson Check – Page No. 356

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Page No. 357
• Mid-Chapter Checkpoint Lesson Check – Page No. 358

Lesson 6: Compare Fractions Using Benchmarks

• Compare Fractions Using Benchmarks – Page No. 361
• Compare Fractions Using Benchmarks Lesson Check – Page No. 362
• Compare Fractions Using Benchmarks Lesson Check 1 – Page No. 363
• Compare Fractions Using Benchmarks Lesson Check 2 – Page No. 364

Lesson 7: Compare Fractions

• Compare Fractions – Page No. 367
• Compare Fractions Lesson Check – Page No. 368
• Compare Fractions Lesson Check 1 – Page No. 369
• Compare Fractions Lesson Check 2 – Page No. 370

Lesson 8: Compare and Order Fractions

• Compare and Order Fractions – Page No. 373
• Compare and Order Fractions Lesson Check – Page No. 374
• Compare and Order Fractions Lesson Check 1 – Page No. 375
• Compare and Order Fractions Lesson Check 2- Page No. 376

Review/Test

• Review/Test – Page No. 377
• Review/Test – Page No. 378
• Review/Test – Page No. 379
• Review/Test – Page No. 380
• Review/Test – Page No. 381
• Review/Test – Page No. 382
• Review/Test – Page No. 387
• Review/Test – Page No. 388

Common Core – Equivalent Fractions – Page No. 331

Equivalent Fractions
Use the model to write an equivalent fraction.

Question 1.

\(\frac{4}{6}=\frac{2}{3}\)

Answer:
\(\frac{4}{6}=\frac{2}{3}\)

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.

\(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)

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.
\(\frac{8}{10}\) _______ \(\frac{4}{5}\)

Answer:
\(\frac{8}{10}\) = \(\frac{4}{5}\)

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.
\(\frac{1}{2}\) _______ \(\frac{7}{12}\)

Answer:
\(\frac{1}{2}\) ≠ \(\frac{7}{12}\)

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.
\(\frac{2}{6}\) _______ \(\frac{4}{12}\)

Answer:
\(\frac{2}{6}\) = \(\frac{4}{12}\)

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.
\(\frac{20}{100}\) _______ \(\frac{1}{5}\)

Answer:
\(\frac{20}{100}\) = \(\frac{1}{5}\)

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.
\(\frac{5}{8}\) _______ \(\frac{9}{10}\)

Answer:
\(\frac{5}{8}\) ≠ \(\frac{9}{10}\)

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:
___________

Answer:
\(\frac{2}{3}\) 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. \(\frac{3}{4}\)

Answer:
a. \(\frac{1}{4}\)

Explanation:
As per the given data,
A rectangle is divided into 8 equal parts
Two parts are shaded
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

Answer:
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

Answer:
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

Answer:
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

Answer:
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

Answer:
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:
___________

Answer:

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:
___________

Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\) = \(\frac{80}{100}\)

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:
___________

Answer:
\(\frac{2}{4}\) = \(\frac{4}{8}\) = \(\frac{8}{16}\)

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:
___________

Answer:
\(\frac{3}{6}\) = \(\frac{6}{12}\) = \(\frac{12}{24}\)

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:
___________

Answer:
\(\frac{3}{10}\) = \(\frac{6}{20}\) = \(\frac{12}{40}\)

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:
___________

Answer:
\(\frac{2}{5}\) = \(\frac{4}{10}\) = \(\frac{8}{20}\)

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.
\(\frac{1}{5}\) ______ \(\frac{4}{10}\)

Answer:
\(\frac{1}{5}\) ≠ \(\frac{4}{10}\)

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.
\(\frac{1}{4}\) ______ \(\frac{2}{8}\)

Answer:
\(\frac{1}{4}\) = \(\frac{2}{8}\)

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.
______

Answer:
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:
_________

Answer:
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:
_________

Answer:
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.

Answer:
\(\frac{2}{6}\) 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:
_________

Answer:
\(\frac{4}{6}\) 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.
\(\frac{1}{4}\) ______ \(\frac{3}{12}\)

Answer:
\(\frac{1}{4}\) = \(\frac{3}{12}\)

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.
\(\frac{4}{5}\) ______ \(\frac{5}{10}\)

Answer:
\(\frac{4}{5}\) ≠ \(\frac{5}{10}\)

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.
\(\frac{3}{8}\) ______ \(\frac{2}{6}\)

Answer:
\(\frac{3}{8}\) ≠ \(\frac{2}{6}\)

Explanation:
3/8 ≠ 2/6

Question 8.
\(\frac{3}{4}\) ______ \(\frac{6}{8}\)

Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)

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

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

Answer:
\(\frac{5}{6}\) = \(\frac{10}{12}\)

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

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

Answer:
\(\frac{6}{12}\) ≠ \(\frac{5}{8}\)

Explanation:
6/12 ≠ 5/8

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

Answer:
\(\frac{2}{5}\) = \(\frac{4}{10}\)

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.
\(\frac{2}{4}\) ______ \(\frac{3}{12}\)

Answer:
\(\frac{2}{4}\) ≠ \(\frac{3}{12}\)

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. \(\frac{2}{2}\)

Answer:
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. \(\frac{2}{8}, \frac{3}{12}\)

Answer:
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

Answer:
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

Answer:
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:
a. Add 2, add 3.
b. Add 6, subtract 3.
c. Subtract 6, add 3.
d. Subtract 2, add 3

Answer:
d. Subtract 2, add 3

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.
\(\frac{8}{10}\) = \(\frac { 8÷□ }{ 10÷□ } \) = \(\frac{□}{□}\)
\(\frac{□}{□}\)

Answer:
\(\frac{4}{5}\)

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.
\(\frac{6}{12}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{2}\)

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.
\(\frac{2}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{5}\)

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.
\(\frac{6}{8}\)
\(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\)

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.
\(\frac{4}{6}\)
\(\frac{□}{□}\)

Answer:
\(\frac{2}{3}\)

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.
\(\frac{10}{12}\)
\(\frac{□}{□}\)

Answer:
\(\frac{5}{6}\)

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.
\(\frac{20}{100}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{5}\)

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.
\(\frac{2}{8}\)
______

Answer:
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.
\(\frac{9}{12}\)
______

Answer:
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.
\(\frac{5}{6}\)
______

Answer:
Yes

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

Question 13.
\(\frac{4}{10}\)
______

Answer:
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

Answer:
\(\frac{2}{3}\) 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?
\(\frac{□}{□}\)

Answer:
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:
_________

Answer:
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

Answer:
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

Answer:
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

Answer:
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.

Answer:
\(\frac{3}{5}\)

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.
\(\frac{6}{8}\) = \(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\)

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.
\(\frac{5}{5}\) = \(\frac{□}{□}\)

Answer:
\(\frac{1}{1}\) = 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.
\(\frac{8}{12}\) = \(\frac{□}{□}\)

Answer:
\(\frac{2}{3}\)

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.
\(\frac{100}{100}\) = \(\frac{□}{□}\)

Answer:
\(\frac{1}{1}\) = 1

Explanation:
The simplest form of 100/100 = 1

Question 6.
\(\frac{2}{6}\) = \(\frac{□}{□}\)

Answer:
\(\frac{1}{3}\)

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.
\(\frac{6}{12}\) _______ \(\frac{1}{12}\)

Answer:
\(\frac{6}{12}\) ≠ \(\frac{1}{12}\)

Explanation:
6/12 ≠ 1/12

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.
\(\frac{3}{12}\) _______ \(\frac{1}{3}\)

Answer:
\(\frac{3}{12}\) ≠ \(\frac{1}{3}\)

Explanation:
3/12 ≠ 1/3

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

Answer:
\(\frac{6}{10}\) = \(\frac{60}{100}\)

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.
\(\frac{11}{12}\) _______ \(\frac{9}{10}\)

Answer:
\(\frac{11}{12}\) ≠ \(\frac{9}{10}\)

Explanation:
11/12 ≠ 9/10

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

Answer:
\(\frac{2}{5}\) = \(\frac{8}{20}\)

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.
\(\frac{4}{8}\) _______ \(\frac{1}{2}\)

Answer:
\(\frac{4}{8}\) = \(\frac{1}{2}\)

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. \(\frac{12}{6}\)

Answer:
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. \(\frac{2}{12}\)

Answer:
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.

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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

• Common Core – Model Factors – Page No. 283
• Common Core – Factors – Page No. 284
• Page No. 287
• Page No. 288

Lesson 2: Factors and Divisibility

• Common Core – Factors and Divisibility – Page No. 289
• Common Core – Factors – Page No. 290
• Page No. 293
• Page No. 294

Lesson 3: Problem Solving • Common Factors

• Common Core – Common Factors – Page No. 295
• Common Core – Common Factors – Page No. 296
• Page No. 297
• Page No. 298
• Page No. 301
• Page No. 302

Lesson 4: Factors and Multiples

• Common Core – Factors and Multiples – Page No. 303
• Common Core – Factors and Multiples – Page No. 304
• Page No. 307
• Page No. 308

Lesson 5: Prime and Composite Numbers

• Common Core – Prime and Composite Numbers – Page No. 309
• Common Core – Prime and Composite Numbers – Page No. 310
• Page No. 313
• Page No. 314

Lesson 6: Algebra • Number Patterns

• Common Core – Number Patterns – Page No. 315
• Common Core – Number Patterns – Page No. 316

Chapter 5 Review/Test

• Review/Test – Page No. 317
• Review/Test – Page No. 318
• Review/Test – Page No. 319
• Review/Test – Page No. 320
• Review/Test – Page No. 321
• Review/Test – Page No. 322
• Page No. 329
• Page No. 330

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

Answer: a

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.

Answer:
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.

Answer: 1,2,4,8

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?

Answer: 1,2,4,8,16

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?

Answer: 28

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.

Answer: Yes

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?
Answer: 37 hours

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?

Answer: 13 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.

Answer: No

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?

Answer: 3

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

Answer: b

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

Answer: c

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

Answer: True

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

Answer: 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

Answer: True.

Explanation: 4×7=28.

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

Answer: True.

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

Answer:

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
Answer: Yes

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

Question 3.
20
Answer: No

Explanation: 20 is not a multiple of 8

Question 4.
40
Answer: Yes

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

Answer: Multiple

Explanation: 6×4=24

Question 9.
36

Answer: Neither

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

Question 10.
48

Answer: Factor

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

Answer: d

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

Answer: 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

Answer: 2

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

Answer: a

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

Answer: d

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

Answer: b

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 _________ .

Answer: Composite number.

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?

Answer: Prime number.

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

Question 3.
73

Answer: Prime number

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

Question 4.
69

Answer: Composite number.

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

Question 5.
42

Answer: Composite number.

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

Answer: Composite number.

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

Answer: Composite number.

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

Answer: Prime number.

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

Question 12.
52

Answer: Composite number.

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

Answer: Composite number.

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.

Answer: False.

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.

Answer: False

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?

Answer: 97

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.

Answer:
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

Answer: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97.

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.

Answer:

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

Answer: Composite number.

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

Answer: Composite number.

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

Answer: Composite number.

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

Answer: Composite number.

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

Answer: Prime number.

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

Question 7.
77

Answer: Composite number.

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

Question 8.
59

Answer: Prime number

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

Question 11.
49

Answer: Composite Number.

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

Question 12.
73

Answer: Prime number.

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?

Answer: Composite number

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?

Answer: No

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

Answer: Prime number.

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

Answer: d

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

Answer: c

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

Answer: b

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

Answer: c

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

Answer: b

Page No. 313

Use the rule to write the numbers in the pattern.

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

Answer: 100,90,80,70,60,..

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 , _____ , _____ , _____ , _____ , …….

Answer: 4,8,16,32,64,…

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 , _____ , _____ , _____ , _____ , …….

Answer: 12,18,24,30,36,…

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

Answer:
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.
5. Rule: Add 2, add 1. First term: 12

Answer: 12,14,15,17,19,21,22,24,25,27,28,30,31.

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

Page No. 314

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 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

• Common Core – Page No. 201
• Common Core – Lesson Check – Page No. 202

Chapter 4 Divide by 1-Digit Numbers – Lesson: 2

• Page No. 205
• Page No. 206

Chapter 4 Divide by 1-Digit Numbers – Lesson: 3

• Common Core – Page No. 207
• Common Core -Lesson Check – Page No. 208

Chapter 4 Divide by 1-Digit Numbers – Lesson: 4

• Common Core – Page No. 211
• Page No. 212

Chapter 4 Divide by 1-Digit Numbers – Lesson: 5

• Interpret the Remainder – Common Core – Page No. 213
• Common Core – Lesson Check – Page No. 214

Chapter 4 Divide by 1-Digit Numbers – Lesson: 6

• Page No. 216
• Page No. 217

Chapter 4 Divide by 1-Digit Numbers – Lesson: 7

• Page No. 218
• Divide Tens, Hundreds, and Thousands – Common Core – Page No. 219
• Common Core – Lesson Check – Page No. 220

Chapter 4 Divide by 1-Digit Numbers – Lesson: 8

• Page No. 222
• Page No. 223
• Page No. 224

Chapter 4 Divide by 1-Digit Numbers – Lesson: 9

• Estimate Quotients Using Compatible Numbers – Common Core – Page No. 224
• Common Core – Lesson Check – Page No. 226

Chapter 4 Divide by 1-Digit Numbers – Lesson: 10

• Model the division on the grid – Page No. 229
• Page No. 230

Chapter 4 Divide by 1-Digit Numbers – Lesson: 11

• Division and the Distributive Property – Common Core – Page No. 231
• Common Core – Lesson Check – Page No. 232

Mid Chapter Checkpoint

• Mid Chapter Checkpoint – Page No. 233
• Mid Chapter Checkpoint – Page No. 234

Chapter 4 Divide by 1-Digit Numbers – Lesson: 12

• Use repeated subtraction to divide – Page No. 237
• Use repeated subtraction to divide – Page No. 238

Chapter 4 Divide by 1-Digit Numbers – Lesson: 13

• Divide Using Repeated Subtraction – Common Core – Page No. 239
• Common Core – Lesson Check – Page No. 240

Chapter 4 Divide by 1-Digit Numbers – Lesson: 14

• Page No. 243
• Page No. 244

Chapter 4 Divide by 1-Digit Numbers – Lesson: 15

• Divide Using Partial Quotients – Common Core – Page No. 245
• Common Core – Lesson Check – Page No. 246

Chapter 4 Divide by 1-Digit Numbers – Lesson: 16

• Page No. 249
• Page No. 250

Chapter 4 Divide by 1-Digit Numbers – Lesson: 17

• Model Division with Regrouping – Common Core – Page No. 251
• Common Core – Lesson Check – Page No. 252

Chapter 4 Divide by 1-Digit Numbers – Lesson: 18

• Page No. 255
• Page No. 256

Chapter 4 Divide by 1-Digit Numbers – Lesson: 19

• Place the First Digit – Common Core – Page No. 257
• Common Core – Lesson Check – Page No. 258

Chapter 4 Divide by 1-Digit Numbers – Lesson: 20

• Page No. 261
• Page No. 262

Chapter 4 Divide by 1-Digit Numbers – Lesson: 21

• Divide by 1-Digit Numbers – Common Core – Page No. 263
• Common Core – Lesson Check – Page No. 264

Chapter 4 Divide by 1-Digit Numbers – Lesson: 22

• Page No. 267
• Page No. 268

Chapter 4 Divide by 1-Digit Numbers – Lesson: 23

• Problem Solving Multistep Division Problems – Common Core – Page No. 269
• Common Core – Lesson Check – Page No. 270

Chapter 4 – Review/Test

• Review/Test – Page No. 271
• Review/Test – Page No. 272
• Review/Test – Page No. 273
• Review/Test – Page No. 274
• Review/Test – Page No. 275
• Review/Test – Page No. 276
• Review/Test – Page No. 280
• Review/Test – Page No. 281
• Review/Test – Page No. 282

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

Answer: 48 crayons

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

Answer: c. 2,319

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:
___________

Answer: 400

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:
___________

Answer: 40

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 = ______

Answer: 500

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 = ______

Answer: 70

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 = ______

Answer: 800

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 = ______

Answer:

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

Answer: 7

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

Answer: 120

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

Answer: 9

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.
______

Answer: 10

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

Answer: 100 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

Answer: 60 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

Answer:

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.
______

Answer: No Mr. Roberts cannot buy the penny in one year.

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:
___________

Answer: 3 months

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

Answer: 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

Answer: b. 3,500

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

Answer: 247

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

Answer: 318

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 _____

Answer:

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 _____

Answer:

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 _____

Answer:

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 _____

Answer:

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 _____

Answer:

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

Answer: b. 1,300

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

Answer: 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

Answer: a. 4 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

Answer: 14

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

Answer: 7 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

Answer: 30

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 adults = 2
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
The total cost of the trip = $1,668 + $50 = $1,718

Question 5.
Mae read 976 pages in 8 weeks. She read the same number of pages each week. How many pages did she read each week?
Options:
a. 109
b. 120
c. 122
d. 984

Answer: c. 122

Explanation:
Total number of pages = 976
Number of weeks = 8
Number of pages Mae read in each week = 976 ÷ 8 = 122

Question 6.
Yolanda and her 3 brothers shared a box of 156 toy dinosaurs. About how many dinosaurs did each child get?
Options:
a. 40
b. 50
c. 60
d. 80

Answer: b. 50

Explanation:
Total number of  toy dinosaurs = 156
Number of brothers = 3
Number of toy dinosaurs each brother got = 156 ÷ 3 = 50

Page No. 271

Question 1.
There are 9 showings of a film about endangered species at the science museum. A total of 459 people saw the film. The same number of people were at each showing. About how many people were at each showing? Select the numbers the quotient is between.

Options:
A. 40
B. 50
C. 60
D. 70
E. 80

Answer: B. 50 C. 60 The quotient is between 50 and 60

Explanation:
Number of people at the showings = 459
Number of showings of a film = 9
Number of people at each showing = Quotient of 459 ÷ 9 = 51

Question 2.
Between which two numbers is the quotient of 87 ÷ 5? Write the numbers in the boxes.

The quotient is between _____ and _____.

Answer: The quotient is between 15 and 20.

Explanation:

Therefore the quotient is 17 and the remainder is 2.

Question 3.
Look at the model. What division does it show?

_____ ÷ _____ = _____ r _____

Answer: 19 ÷ 3 = 6 r 1

Explanation:
Count the total number of counters =Dividend = 19
Number of circles = Divisor = 3
After the distribution of the counters,
The quotient is 6 because in each circle there are 6 counters
The leftover counter is the remainder = 1

For 4a–4d, choose Yes or No to tell whether the division sentence has a remainder.

Question 4.
a. 28 ÷ 4
i. yes
ii. no

Answer: ii. no

Explanation:

Therefore the quotient is 7 and the remainder is 0

Question 4.
b. 35 ÷ 2
i. yes
ii. no

Answer: i. yes

Explanation:

Therefore the quotient is 17 and the remainder is 1

Question 4.
c. 40 ÷ 9
i. yes
ii. no

Answer: i. yes

Explanation:

Therefore the quotient is 4 and the remainder is 4

Question 4.
d. 45 ÷ 5
i. yes
ii. no

Answer: ii. no

Explanation:

Therefore the quotient is 5 and the remainder is 0

Page No. 272

Question 5.
A park guide plans the swan boat rides for 40 people. Each boat can carry 6 people at a time. What is the best way to interpret the remainder in this situation so that everyone gets a ride?
Type below:
____________

Answer: 4 people are leftover after the boat takes 6 people at a time for a ride, therefore, these four people go on the ride in the next round.

Explanation:
Quotient:
A. Use 40 counters to represent the 40 people. 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 40 ÷ 6
D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6
Therefore, the quotient is 6 and the remainder is 4
It means that the boat takes 7 rounds in which 6 are filled with 6 people while 4 people are leftover they take the last ride.

Question 6.
Nolan divides his 88 toy cars into boxes. Each box holds 9 cars. How many boxes does Nolan need to store all of his cars?
______ boxes

Answer: 10

Explanation:
Total number of toys Nolan has = 88
Number of cars placed in each box  = 9
Number of boxes = 88 ÷ 9 = 9.7 = 10 (approx)
We take approximate value because all the toys must be fit in the box.

A group of 140 tourists are going on a tour. The tour guide rents 15 vans. Each van holds 9 tourists.

Question 7.
Part A
Write a division problem that can be used to find the number of vans needed to carry the tourists. Then solve.
Type below:
____________

Answer: 140 divided by 9 gives the number of vans  needed to carry the tourists

Explanation:

Total number of tourists = 140
Number of students who fit in each van = 9
Number of vans = Quotient of 150 ÷ 9 = 15
The leftover of tourists = Remainder =5
Can be placed in a different van or can be adjusted in the 15 vans.

Question 7.
Part B
What does the remainder mean in the context of the problem?
Type below:
____________

Answer: The leftover of tourists = Remainder =5

Explanation:
The leftover of tourists= Remainder =5
Can be placed in a different van or can be adjusted in the 15 vans.

Question 7.
Part C
How can you use your answer to determine if the tour guide rented enough vans? Explain.
Type below:
____________

Answer: The number of vans would be correct if they were 16 instead of 15

Explanation:
Then the answer can be determined as all the 140  tourists have enjoyed their trip to the fullest and traveled comfortably without any hassle and bustle.

Question 8.
Solve.
3,200 ÷ 8 = ______

Answer: 400

Explanation:

Therefore we can say that the quotient is 400 while the remainder is 0

Page No. 273

Question 9.
Which quotients are equal to 300? Mark all that apply.
Options:
a. 1,200 ÷ 4
b. 180 ÷ 9
c. 2,400 ÷ 8
d. 2,100 ÷ 7
e. 90 ÷ 3
f. 3,000 ÷ 3

Answer: a. 1,200 ÷ 4, c. 2,400 ÷ 8, d. 2,100 ÷ 7

Explanation:

1,200 ÷ 4

Therefore the quotient is 300 and the remainder is 0.

2,400 ÷ 8

Therefore the quotient is 300 and the remainder is 0.

2,100 ÷ 7

Therefore the quotient is 300 and the remainder is 0.

Question 10.
Margo estimated 188 ÷ 5 to be between 30 and 40. Which basic facts did she use to help her estimate? Mark all that apply.
Options:
a. 10 ÷ 5
b. 15 ÷ 5
c. 20 ÷ 5
d. 25 ÷ 5

Answer: b. 15 ÷ 5 c. 20 ÷ 5

Explanation:
188 ÷ 5
STEP 1 Identify the basic fact. 15 ÷ 5
STEP 2 Use place value. 150 = 15 tens
STEP 3 Divide. 15 tens ÷ 5 = 3 tens
150 ÷ 3 = 30

STEP 1 Identify the basic fact. 20 ÷ 5
STEP 2 Use place value. 200 = 20 tens
STEP 3 Divide. 20 tens ÷ 5 = 4 tens
200 ÷ 5 = 40

Therefore we can say that the quotient is between 30 to 40

For 12a–12d, choose Yes or No to show how to use the Distributive Property to break apart the dividend to find the quotient 132 ÷ 6.

Question 12.
a. (115 ÷ 6) + (17 ÷ 6)
i. yes
ii. no

Answer: ii. no

Explanation:
According to the question, the nearest estimates are 115 and 17 but these are not divisible by 6.

Question 12.
b. (100 ÷ 6) + (32 ÷ 6)
i. yes
ii. no

Answer: ii. no

Explanation:
According to the question, the nearest estimates are 100 and 32 but these are not divisible by 6.

Question 12.
c. (90 ÷ 6) + (42 ÷ 6)
i. yes
ii. no

Answer: i. yes

Explanation:
STEP1 Find the nearest estimates of the number 132
STEP2 We can break the number 132 into 90 + 42
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (90 ÷ 6) + (42 ÷ 6)
STEP5 Add quotients of the above 15 +7= 22

Question 12
d. (72 ÷ 6) + (60 ÷ 6)
i. yes
ii. no

Answer: i. yes

Explanation:
STEP1 Find the nearest estimates of the number 132
STEP2 We can break the number 132 into 72 + 60
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (72 ÷ 6) + (60 ÷ 6)
STEP5 Add quotients of the above 12 +10= 22

Question 13.
There are 60 people waiting for a river raft ride. Each raft holds 15 people. Silvia used the work below to find the number of rafts needed. Explain how Silvia’s work can be used to find the number of rafts needed.

Type below:
_________

Answer: 4

Explanation:
Total number of people = 60
Number of people each river raft can hold = 15
Number of rafts needed to give a ride to all the people = 60 ÷ 15 = 4

Page No. 274

A travelling circus brings along everything it needs for a show in big trucks.

Question 14.
Part A
The circus sets up chairs in rows with 9 seats in each row. How many rows will need to be set up if 513 people are expected to attend the show?
______ rows

Answer: 57

Explanation:
The total number of people = 513
Number of seats in each row = 9
Number of rows = 513 ÷ 9 = 57

Question 14.
Part B
Can the rows be divided into a number of equal sections? Explain how you found your answer.
Type below:
_________

Answer: Yes, the rows can be divided into equal sections. 57 ÷ 3 = 19

Explanation:
We can divide 57 using the divisor as 3, then the quotient is 19 and the remainder is 0.

Question 14.
Part C
Circus horses eat about 250 pounds of horse food per week. About how many pounds of food does a circus horse eat each day? Explain.
About ______ pounds

Answer: About 35 pounds

Explanation:
Mass of food the horses ate in one week = 250 pounds
Number of days in a week =7
Mass of food the horses ate per day = Quotient of 250 ÷  7 = about 35

Question 15.
Hilda wants to save 825 digital photographs in an online album. Each folder of the album can save 6 photographs. She uses division to find out how may full folders she will have. In what place is the first digit of the quotient?
_________

Answer: Hundreds place

Explanation:
Use place value to place the first digit. Look at the hundreds in 825. 800 hundred can be shared among 6 groups
without regrouping.
Now there is 80 tens and 25 ones to share among 6 groups.
The first digit of the quotient will be in the hundreds place.

Page No. 275

Question 16.
Which model matches each expression? Write the letter in the box next to the model.

Answer: 1st picture – 150 ÷ 30
2nd picture – 160 ÷ 40
3rd picture – 150 ÷ 50
4th picture – 160 ÷ 80

Explanation:
150 ÷ 30

160 ÷ 40

150 ÷ 50

160 ÷ 80

Question 17.
Popcorn was donated for the school fair by 3 different popcorn vendors. They donated a total of 636 bags of popcorn. Each vendor donated the same number of bags. How many bags of popcorn did each vendor donate?
______ bags

Question 18.
Use partial quotients. Fill in the blanks.

Answer: 212

Explanation:
Total number of popcorn bags = 636
Number of popcorn vendors = 3
Number of popcorn bags donated by each vendor = 636 ÷ 3 = 212

Therefore the number of bags donated by each vendor = 212

Page No. 276

Question 19.
Zack needs to divide these base-ten blocks into 3 equal groups.

Draw or describe a model to show how many are in each group.
Type below:
________

Answer: 16

Explanation:
Total number of counters = 48
Number of groups they are supposed to be divided = 3
Then, 48 ÷ 3

Therefore the quotient is 16 and the remainder is 0.

Question 20.
Jim needs to divide 750 coupon books equally among 9 stores. In which place is the first digit of the quotient? Choose the word that makes the sentence true.
The first digit of the quotient is in the place.
________

Answer: tens place

Explanation:
Use place value to place the first digit. Look at the hundreds in 750. 720 hundred can be shared among 9 groups
without regrouping.
Now there is 72 tens and 30 ones to share among 9 groups.
The first digit of the quotient will be in the tens place.

Page No. 280

Question 1.
Use the arrays to name the factors of 12.
a.
_____ × _____ = 12

Answer: 6 x 2 = 12

Explanation:
There are a total of 12 counters in the given figure.
So, we can see that 6 + 6 = 12 from the above figure.
Hence we can write as 6 x 2 = 12

Question 1.
b.
_____ × _____ = 12

Question 1.

Answer: 4 x 3 = 12

Explanation:
The number of columns and rows are 4 and 3 respectively.
So we can calculate the multiplication by 4 x 3 = 12

c.
_____ × _____ = 12

Answer: 6 x 2 = 12

Explanation:
The number of columns and rows are 4 and 3 respectively.
So we can calculate the multiplication by 4 x 3 = 12.

Use tiles to find all the factors of the product. Record the arrays and write the factors shown.

Question 2.
5: __________
Type below:
________

Answer:

Explanation:

Question 3.
20: __________
Type below:
________

Answer:

Explanation:

Question 4.
25: __________
Type below:
________

Answer:

Explanation:

Page No. 281

Practice: Copy and Solve Use tiles to find all the factors of the product. Record the arrays on grid paper and write the factors shown.

Question 5.
9: ______________
Type below:
________

Answer:

Explanation:

Question 6.
21: ______________
Type below:
________

Answer:

Explanation:

Question 7.
17: ______________
Type below:
________

Answer:

Explanation:

Question 8.
18: ______________
Type below:
________

Answer:

Explanation:

Use the diagram for 9–10.

Question 9.
Pablo is using 36 tiles to make a patio. Can he arrange the tiles in another way and show the same factors? Draw a quick picture and explain.
Type below:
________

Answer:

Explanation:

Question 10.
How many different rectangular arrays can Pablo make with all 36 tiles, so none of the arrays show the same factors?
________ rectangular arrays

Answer:

Explanation:

Question 11.
If 6 is a factor of a number, what other numbers must be factors of the number?
Type below:
________

Answer:

Explanation:

Question 12.
Jean spent $16 on new T-shirts. If each shirt cost the same whole-dollar amount, how many could she have bought?
Type below:
________

Answer:

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:
________

Answer:

Explanation:

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

Answer:

Explanation:

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

Answer:

Explanation:

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

Answer:

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:
________

Answer:

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

Answer:

Explanation:

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

Answer:

Explanation:

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

Answer:

Explanation:

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

Answer:

Explanation:

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

Answer:

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.