# Go Math Grade 5 Answer Key Chapter 1 Place Value, Multiplication, and Expressions

## Go Math Grade 5 Answer Key Chapter 1 Place Value, Multiplication, and Expressions

It’s really difficult to find Solutions for all the Problems in Go Math Grade 5 Chapter 1 all in one place. Now, you will no longer have such difficulties. We are providing Go Math Grade 5 Answer Key Chapter 1 Place Value, Multiplication, and Expressions. Check out Step by Step Solutions provided for various lessons and the topics in it. Practice using the 3rd Grade Go Math Answer Key Ch 1 Place Value, Multiplication, and Expressions and score better grades in the exam.

Lesson 1: Investigate • Place Value and Patterns

Lesson 2: Place Value of Whole Numbers

Lesson 3: Algebra • Properties

Lesson 4: Algebra • Powers of 10 and Exponents

Lesson 5: Algebra • Multiplication Patterns

Mid-Chapter Checkpoint

Lesson 6: Multiply by 1-Digit Numbers

Lesson 7: Multiply by Multi-Digit Numbers

Lesson 8: Relate Multiplication to Division

Lesson 9: Problem Solving • Multiplication and Division

Lesson 10: Algebra • Numerical Expressions

Lesson 11: Algebra • Evaluate Numerical Expressions

Lesson 12: Algebra • Grouping Symbols

Review/Test

### Place Value and Patterns – Share and Show – Page No. 7

Complete the sentence.

Question 1.
500 is 10 times as much as ______

50

Explanation:
Let the unknown number is S.
500 = 10S
S = 500/10 = 50.
500 is 10 times as much as 50.

Question 2.
20,000 is $$\frac{1}{10}$$ of ______

2,00,000

Explanation:
Let the unknown number is S.
20,000 = $$\frac{1}{10}$$ S
S = 20,000 X 10 = 2,00,000

Use place-value patterns to complete the table

Question 5.

 Numbers 10 times as much as $$\frac{1}{10}$$ of 10 ______ ______ 3,000 ______ ______ 800 ______ ______ 50 ______ ______

 Numbers 10 times as much as $$\frac{1}{10}$$ of 10 ___1___ ___100___ 3,000 ___300___ ___30,000___ 800 ___80___ ___8,000___ 50 ___5___ ___500___

Explanation:
1. 10 is 10 times as much as ______
Let the unknown number is S.
10 = 10S
S = 10/10 = 1.
10 is 10 times as much as 1.
10 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
10 = $$\frac{1}{10}$$ S
S = 10 X 10 = 100.
2. 3,000 is 10 times as much as ______
Let the unknown number is S.
3,000 = 10S
S = 3,000/10 = 300.
3,000 is 10 times as much as 300.
3,000 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
3,000 = $$\frac{1}{10}$$ S
S = 3,000 X 10 = 30,000.
3. 800 is 10 times as much as ______
Let the unknown number is S.
800 = 10S
S = 800/10 = 80.
800 is 10 times as much as 80.
800 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
800 = $$\frac{1}{10}$$ S
S = 800 X 10 = 8,000.
4. 50 is 10 times as much as ______
Let the unknown number is S.
50 = 10S
S = 50/10 = 5.
50 is 10 times as much as 5.
50 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
50 = $$\frac{1}{10}$$ S
S = 50 X 10 = 500.

Question 6.

 Numbers 10 times as much as $$\frac{1}{10}$$ of 400 ______ ______ 90 ______ ______ 6,000 ______ ______ 200 ______ ______

 Numbers 10 times as much as $$\frac{1}{10}$$ of 400 __40____ ___4,000___ 90 ___9___ ___900___ 6,000 __600____ __60,000____ 200 ___20___ ___2,000___

Explanation:
1. 400 is 10 times as much as ______
Let the unknown number is S.
400 = 10S
S = 400/10 = 40.
400 is 10 times as much as 40.
400 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
400 = $$\frac{1}{10}$$ S
S = 400 X 10 = 4,000.
2. 90 is 10 times as much as ______
Let the unknown number is S.
90 = 10S
S = 90/10 = 9.
90 is 10 times as much as 9.
90 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
90 = $$\frac{1}{10}$$ S
S = 90 X 10 = 900.
3. 6,000 is 10 times as much as ______
Let the unknown number is S.
6,000 = 10S
S = 6,000/10 = 600.
6,000 is 10 times as much as 600.
6,000 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
6,000 = $$\frac{1}{10}$$ S
S = 6,000 X 10 = 60,000.
4. 200 is 10 times as much as ______
Let the unknown number is S.
200 = 10S
S = 200/10 = 20.
200 is 10 times as much as 20.
200 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
200 = $$\frac{1}{10}$$ S
S = 200 X 10 = 2,000.

Complete the sentence with 100 or 1,000.

Question 13.
200 is ______ times as much as 2

200 is 100 times as much as 2

Explanation:
Let the unknown number be S.
200 = 2S
S = 200/2 = 100

Question 16.
600 is ______ times as much as 6

600 is 100 times as much as 6

Explanation:
Let the unknown number be S.
600 = 6S
S = 600/6= 100

Question 17.
50,000 is ______ times as much as 500

50,000 is 100_ times as much as 500

Explanation:
Let the unknown number be S.
50,000 = 500S
S = 50,000/500= 100

Question 18.
30,000 is ______ times as much as 30

30,000 is 1,000 times as much as 30

Explanation:
Let the unknown number be S.
30,000 = 30S
S = 30,000/30 = 1,000

### Place Value and Patterns – Problem Solving – Page No. 8

Sense or Nonsense?

Question 20.
Mark and Robyn used base-ten blocks to show that 300 is 100 times as much as 3. Whose model makes sense? Whose model is nonsense? Explain your reasoning.

Type below:
__________

Robyn’s model makes sense. Because the given data 300 is 100 times as much as 3. It clearly states that there are 100 model-blocks and one model blocks should take to solve the problem.

Question 20.
Explain how you would help Mark understand why he should have used small cubes instead of longs.
Type below:
__________

Mark’s drew 100 model-blocks and 10 model-blocks which. To get 300 is 100 times as much as 3, he needs to do 300/3 = 100 model blocks.

### Place Value of Whole Numbers – Share and Show – Page No. 11

Complete the place-value chart to find the value of each digit.

Question 1.

Type below:
__________

7,333,820

Explanation:
7 x 1,000,000 = 7,000,000
3 x 100,000 = 300,000
3 x 1,000 = 3000
8 x 100 = 800
2 x 10 = 20

Write the value of the underlined digit.

Question 2.
1,574,833
__________

4,000

Explanation:
(1 x 1,000,000) + (5 x 1,00,000) + (7 x 10,000) + (4 x 1,000) + (8 x 100) + (3 x 10) + (3 x 1)
4 x 1,000 = 4 thousands = 4,000

Question 5.
301,256,878
__________

3,00,000,000

Explanation:
(3 x 1,00,000,000) + (0 x 10,000,000) + (1 x 1,000,000) + (2 x 1,00,000) + (5 x 10,000) + (6 x 1,000) + (8 x 100) + (7 x 10) + (8 x 1)
3 x 1,00,000,000 = 3 hundred- millions = 3,00,000,000

Write the number in two other forms.

Question 6.
(8 × 100,000) + (4 × 1,000) + (6 × 1) =
__________

80,4006
Eight Hundred Four Thousand Six

Explanation:
(8 × 100,000) + (4 × 1,000) + (6 × 1) = 800,000 + 4,000 + 6 = 80,4006

Write the value of the underlined digit.

Question 8.
849,567,043
__________

40,000,000

Explanation:
(8 x 1,00,000,000) + (4 x 10,000,000) + (9 x 1,000,000) + (5 x 1,00,000) + (6 x 10,000) + (7 x 1,000) + (0 x 100) + (4 x 10) + (3 x 1)
4 x 10,000,000 = 4 ten- millions = 40,000,000

Question 9.
9,422,850
__________

4,00,000

Explanation:
(9 x 1,000,000) + (4 x 1,00,000) + (2 x 10,000) + (2 x 1,000) + (8 x 100) + (5 x 10) + (0 x 1)
4 x 1,00,000 = 4 Hundred Thousand = 4,00,000

Question 10.
96,283
__________

90,000

Explanation:
(9 x 10,000) + (6 x 1,000) + (2 x 100) + (8 x 10) + (3 x 1)
9 x 10,000 = 9 ten-thousands = 90,000

Question 12.
791,350
__________

300

Explanation:
(7 x 1,00,000) + (9 x 10,000) + (1 x 1,000) + (3 x 100) + (5 x 10) + (0 x 1)
3 x 100 = 3 hundred = 300

Question 13.
27,911,534
__________

7,000,000

Explanation:
(2 x 10,000,000) + (7 x 1,000,000) + (9 x 1,00,000) + (1 x 10,000) + (1 x 1,000) + (5 x 100) + (3 x 10) + (4 x 1)
7 x 1,000,000 = Seven Million = 7,000,000

Question 14.
105,980,774
__________

80,000

Explanation:
(1 x 1,00,000,000) + (0 x 10,000,000) + (5 x 1,000,000) + (9 x 1,00,000) + (8 x 10,000) + (0 x 1,000) + (7 x 100) + (7 x 10) + (4 x 1)
8 x 10,000 = 8 ten-thousand = 80,000

Question 15.
8,265,178
__________

5,000

Explanation:
(8 x 1,000,000) + (2 x 1,00,000) + (6 x 10,000) + (5 x 1,000) + (1 x 100) + (7 x 10) + (8 x 1)
5 x 1,000 = 5 one-thousand = 5,000

Write the number in two other forms.

Question 16.
345,000
Type below:
__________

Three Hundred Forty-Five Thousand
(3 x 1,00,000) + (4 x 10,000) + (5 x 1,000) + (0 x 100) + (0 x 10) + (0 x 1)

Question 17.
119,000,003
Type below:
__________

One Hundred Nineteen Million Three
(1 x 100,000,000) + (1 x 10,000,000) + (9 x 1,000,000) + (0 x 1,00,000) + (0 x 10,000) + (0 x 1,000) + (0 x 100) + (0 x 10) + (3 x 1)

### Place Value of Whole Numbers – Problem Solving – Page No. 12

Use the table for 18–19.

Question 18.
Which planet is about 10 times as far as Earth is from the Sun?

__________

Saturn

Explanation:
Saturn = 1,427,000/10 = 142,700 which is 10 times as far as Earth

Question 19.
Which planet is about $$\frac{1}{10}$$ of the distance Uranus is from the Sun?
__________

Mars

Explanation:
Mars = 227,900
$$\frac{1}{10}$$ x 2,871,000 = 287,100
Which planet is about $$\frac{1}{10}$$ of the distance Uranus is from the Sun

Question 22.
Test Prep In the number 869,653,214, which describes how the digit 6 in the ten-millions place compares to the digit 6 in the hundred-thousands place?
Options:
A. 10 times as much as
B. 100 times as much as
C. 1,000 times as much as
D.$$\frac{1}{10}$$ of

B. 100 times as much as

Explanation:
869,653,214
(8 x 100,000,000) + (6 x 10,000,000) + (9 x 1,000,000) + (6 x 1,00,000) + (5 x 10,000) + (3 x 1,000) + (2 x 100) + (1 x 10) + (4 x 1)
6 x 10,000,000 = 60,000,000
6 x 1,00,000 = 6,00,000
60,000,000/6,00,000 = 100

### Properties – Share and Show – Page No. 15

Use properties to find 4 × 23 × 25.

Question 1.
23 × × 25 ________ Property of Multiplication
23 × ( × ) ________ Property of Multiplication
23 ×
__________
____

23 x 4 x 25; Commutative Property of Multiplication
23 x (4 x 25); Associative Property of Multiplication
23 x 100
2,300

Use properties to find the sum or product.

Question 2.
89 + 27 + 11 = ____

89 + (27 + 11); Associative Property of Addition
89 + 38
127

Question 3.
9 × 52 = ____

468

Explanation:
9 x 52
Write 52 = (50 + 2)
9 x (50 + 2)
(9 x 50) + (9 x 2); Distributive Property of Multiplication
450 + 18
468

Question 4.
107 + 0 + 39 + 13 = ____

107 + 0 + 39 + 13
(107 + 0) + (39 + 13); Associative Property of Addition
107 + 0 = 107; Identity Property of Addition
107 + 52 = 159

Complete the equation, and tell which property you used.

Question 6.
Describe how you can use properties to solve problems more easily.
Type below:
__________

Using Properties of Addition and Properties of Multiplication, we can solve problems more easily. Simplifying problems is easy with the properties.

Practice: Copy and Solve Use properties to find the sum or product.

Question 7.
3 × 78 = ____

234, Associative Property of Multiplication

Explanation:
Write 78 as 6 x 13
3 x 6 x 13
(3 x 6) x 13; Associative Property of Multiplication
18 x 13 = 234

Question 8.
4 × 60 × 5 = ____

1,200; Associative Property of Multiplication

Explanation:
4 x 60 x 5
4 x (60 x 5); Associative Property of Multiplication
4 x 300 = 1,200

Question 9.
21 + 25 + 39 + 5 = ____

Explanation:
(21 + 25) + (39 + 5); Associative Property of Addition
46 + 44 = 90

Complete the equation, and tell which property you used.

Question 10.
11 + (19 + 6) = (11 + ____) + 6

11 + (19 + 6) = (11 + 19) + 6; Associative Property of Addition

Question 11.
25 + 14 = ____ + 25

25 + 14 = 14 + 25; Commutative Property of Addition

Question 12.
Show how you can use the Distributive Property to rewrite and find (32 × 6) + (32 × 4).
____

(32 × 6) + (32 × 4) = 32 x (6 + 4); Distributive Property

### Properties – Problem Solving – Page No. 16

Question 14.
Jacob is designing an aquarium for a doctor’s office. He plans to buy 6 red blond guppies, 1 blue neon guppy, and 1 yellow guppy. The table shows the price list for the guppies. How much will the guppies for the aquarium cost?

$____ Answer:$162

Explanation:
Jacob is designing an aquarium for a doctor’s office. He plans to buy 6 red blond guppies, 1 blue neon guppy, and 1 yellow guppy.
(6 x $22) + (1 x$11) + (1 x $19) =$132 + $11 +$19 = $162 Question 15. Sylvia bought 8 tickets to a concert. Each ticket costs$18. To find the total cost in dollars, she added the product 8 × 10 to the product 8 × 8, for a total of 144. Which property did Sylvia use?
i. Distributive Property
ii. Associative Property

i. Distributive Property

Explanation:
Sylvia bought 8 tickets to a concert. Each ticket costs $18. To find the total cost in dollars = 8 x$18
Using Distributive Property
(8 × 10) + (8 × 8) = 8 x (10 + 8) = 144.

Question 17.
Test Prep Canoes rent for $29 per day. Which expression can be used to find the cost in dollars of renting 6 canoes for a day? Options: A. (6 + 20) + (6 + 9) B. (6 × 20) + (6 × 9) C. (6 + 20) × (6 + 9) D. (6 × 20) × (6 × 9) Answer: B. (6 × 20) + (6 × 9) Explanation: Canoes rent for$29 per day. For renting 6 canoes for a day, 6 x $29 6 x$(20 + 9) = (6 x 20) + (6 x 9)

### Powers of 10 and Exponents – Share and Show – Page No. 18

Write in exponent form and word form.

Question 1.
10 × 10
Exponent form:
Word form:
Type below:
__________

Exponent form: 102
Word form: the second power of ten

Explanation:
10 × 10
Base = 10;
Exponent = 2;
Exponent Form: 102
Word Form: the second power of ten

Find the value.

Question 3.
102 = ____

100

Explanation:
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;

### Powers of 10 and Exponents – On Your Own – Page No. 19

Write in exponent form and word form.

Question 6.
10 × 10 × 10
exponent form:
word form:
Type below:
__________

Exponent form: 103
Word form: the third power of ten

Explanation:
10 × 10 × 10
Base = 10;
Exponent = 3;
Exponent Form: 103
Word Form: the third power of ten

Find the value.

Question 8.
104 = ____

10,000

Explanation:
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;

Question 10.
6 × 104 = ____

60,000

Explanation:
6 × 104
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
6 x 10,000 = 60,000

Complete the pattern.

Question 12.
9 × 100 = _______ = 9
9 × 101 = _______ = 90
9 × 102 = _______ = 900
9 × 103 = _______ = 9,000
9 × 104 = _______ = 90,000

9 × 100 = 9 x 1 = 9
9 × 101 = 9 x 10 = 90
9 × 102 = 9 x 10 x 10 = 900
9 × 103 = 9 x 10 x 10 x 10= 9,000
9 × 104 = 9 x 10 x 10 x 10 x 10 = 90,000

Explanation:
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;

Question 13.
12 × 100 = 12 × 1 = _______
12 × 101 = 12 × 10 = _______
12 × 102 = 12 × 10 × 10 = _______
12 × 103 = 12 × 10 × 10 × 10 _______
12 × 104 = 12 × 10 × 10 × 10 × 10 _______

12 × 100 = 12 × 1 = 12
12 × 101 = 12 × 10 = 120
12 × 102 = 12 × 10 × 10 = 1,200
12 × 103 = 12 × 10 × 10 × 10 = 12,000
12 × 104 = 12 × 10 × 10 × 10 × 10 = 120,000

Explanation:
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;

Question 15.
Explain how to write 50,000 using exponents.
Type below:
__________

5 x 104

Explanation:
5 x 10,000
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
10,000 = 10 x 10 x 10 x 10 = 104
5 x 104

### Powers of 10 and Exponents – UNLOCK the Problem – Page No. 20

Question 16.
Lake Superior is the largest of the Great Lakes. It covers a surface area of about 30,000 square miles. How can you show the estimated area of Lake Superior as a whole number multiplied by a power of ten?

a. What are you asked to find?
Options:
A. 3 × 102 sq mi
B. 3 × 103 sq mi
C. 3 × 104 sq mi
D. 3 × 105 sq mi

C. 3 × 104 sq mi

Explanation:
Lake Superior is the largest of the Great Lakes. It covers a surface area of about 30,000 square miles.
3 x 10,000
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
10,000 = 10 x 10 x 10 x 10 = 104
3 x 104

Question 16.
b. How can you use a pattern to find the answer?
Type below:
__________

3 x 10,000
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
10,000 = 10 x 10 x 10 x 10 = 104
3 x 104

Question 16.
c. Write a pattern using the whole number 3 and powers of ten.
3 × 101 = 3 × 10   =
3 × 102 =              =
3 × 103 =              =
3 × 104 =              =
Type below:
__________

3 × 101 = 3 × 10   =
3 × 102 = 3 x 10 x 10 = 300
3 × 103 = 3 x 10 x 10 x 10 = 3,000
3 × 104 = 3 x 10 x 10 x 10 x 10 = 30,000

Question 16.
d. Fill in the correct answer choice above.
Type below:
__________

3 × 104 = 3 x 10 x 10 x 10 x 10 = 30,000

Question 17.
The Earth’s diameter through the equator is about 8,000 miles. What is the Earth’s estimated diameter written as a whole number multiplied by a power of ten?
Options:
A. 8 × 101 miles
B. 8 × 102 miles
C. 8 × 103 miles
D. 8 × 104 miles

C. 8 × 103 miles

Explanation:
The Earth’s diameter through the equator is about 8,000 miles.
8 x 1,000
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
1,000 = 10 x 10 x 10
8 x 1,000 = 8 x 103

Question 18.
The Earth’s circumference around the equator is about 25 × 103 miles. What is the Earth’s estimated circumference written as a whole number?
Options:
A. 250,000 miles
B. 25,000 miles
C. 2,500 miles
D. 250 miles

B. 25,000 miles

Explanation:
The Earth’s circumference around the equator is about 25 × 103 miles.
25 × 103 miles;
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
25 x 1,000 = 25,000 miles

### Multiplication Patterns – Share and Show – Page No. 22

Use mental math and a pattern to find the product.

Question 1.
30 × 4,000 = ____

3 x 4 = 12

Explanation:
30 × 4,000
The basic fact is 3 x 4 = 12

Use mental math to complete the pattern.

Question 2.
1 × 1 = 1
1 × 101 = _______
1 × 102 = _______
1 × 103 = _______

1 × 1 = 1
1 × 101 = 10
1 × 102 = 100
1 × 103 = 1,000

Explanation:
1 × 1 = 1
1 × 101 = 1 x 10 = 10
1 × 102 = 1 x 10 x 10 = 100
1 × 103 = 1 x 10 x 10 x 10 = 1,000

Question 3.
7 × 8 = 56
(7 × 8) × 101 = _______
(7 × 8) × 102 = _______
(7 × 8) × 106 = _______

7 × 8 = 56
(7 × 8) × 101 = 560
(7 × 8) × 102 = 5,600
(7 × 8) × 106 = 56,000,000

Explanation:
7 × 8 = 56
(7 × 8) × 101 = 56 x 10 = 560
(7 × 8) × 102 = 56 x 10 x 10 = 5,600
(7 × 8) × 106 = 56 x 10 x 10 x 10 x 10 x 10 x 10 = 56,000,000

Question 4.
6 × 5 = _______
6 × 5 × _______ = 300
6 × 5 × _______ = 3000
6 × 5 × _______ = 30,000

6 × 5 = 30
6 × 5 × 101 = 300
6 × 5 × 103 = 3000
6 × 5 × 104 = 30,000

Explanation:
6 × 5 = 30
6 × 5 × 10 = 300
6 × 5 × 10 x 10 x 10 = 3000
6 × 5 × 10 x 10 x 10 x 10 = 30,000

Use mental math to complete the pattern.

Question 6.
3 × 7 = 21
(3 × 7) × 101 = _______
(3 × 7) × 102 = _______
(3 × 7) × 103 = _______

3 × 7 = 21
(3 × 7) × 101 = 210
(3 × 7) × 102 = 2,100
(3 × 7) × 103 = 21,000

Explanation:
3 × 7 = 21
(3 × 7) × 101 = 21 x 10 = 210
(3 × 7) × 102 = 21 x 10 x 10 = 2,100
(3 × 7) × 103 = 21 x 10 x 10 x 10 = 21,000

Question 7.
5 × 4 = _______
(5 × 4) × _______ = 200
(5 × 4) × _______ = 2,000
(5 × 4) × _______ = 20,000

5 × 4 = 20
(5 × 4) × 101 = 200
(5 × 4) × 102 = 2,000
(5 × 4) × 103 = 20,000

Explanation:
5 × 4 = 20
(5 × 4) × 10 = 200
(5 × 4) × 10 x 10 = 2,000
(5 × 4) × 10 x 10 x 10 = 20,000

Question 8.
5 × 7 = _______
(5 × 7) × _______ = 350
(5 × 7) × _______ = 3,500
(5 × 7) × _______ = 35,000

5 × 7 = 35
(5 × 7) × 101 = 350
(5 × 7) × 102 = 3,500
(5 × 7) × 103 = 35,000

Explanation:
5 × 7 = 35
(5 × 7) × 10 = 350
(5 × 7) × 10 x 10 = 3,500
(5 × 7) × 10 x 10 x 10 = 35,000

Question 10.
6 × 7 = 42
(6 × 7) × 101 = _______
(6 × 7) × 102 = _______
(6 × 7) × 103 = _______

6 × 7 = 42
(6 × 7) × 101 = 420
(6 × 7) × 102 = 4,200
(6 × 7) × 103 = 42,000

Explanation:
6 × 7 = 42
(6 × 7) × 101 = 42 x 10 = 420
(6 × 7) × 102 = 42 x 10 x 10 = 4,200
(6 × 7) × 103 = 42 x 10 x 10 x 10 = 42,000

Use mental math and a pattern to find the product.

Question 11.
(6 × 6) × 101 = ____

(6 × 6) × 101 =  360

Explanation:
6 x 6 =36
(6 × 6) × 101 = 36 x 10 = 360

Question 14.
(4 × 3) × 102 = ____

1,200

Explanation:
(4 × 3) = 12
(4 × 3) × 101 = 12 x 10 = 120
(4 × 3) × 102 = 12 x 10 x 10 = 1,200

Question 15.
(2 × 5) × 103 = ____

10,000

Explanation:
(2 × 5) = 10
(2 × 5) × 101 = 10 x 10 = 100
(2 × 5) × 102 = 10 x 10 x 10 = 1,000
(2 × 5) × 103 = 10 x 10 x 10 x 10 = 10,000

Question 16.
(2 × 8) × 102 = ____

1,600

Explanation:
(2 × 8) = 16
(2 × 8) × 101 = 16 x 10 = 160
(2 × 8) × 102 = 16 x 10 x 10 = 1,600

Question 17.
(6 × 5) × 103 = ____

30,000

Explanation:
(6 × 5) = 30
(6 × 5) × 101 = 30 x 10 = 300
(6 × 5) × 102 = 30 x 10 x 10 = 3,000
(6 × 5) × 103 = 30 x 10 x 10 x 10 = 30,000

### Multiplication Patterns – Share and Show – Page No. 23

Use mental math to complete the table.

Question 20.
1 roll = 50 dimes ; Think:50 dimes per roll × 20 rolls =(5 × 2) × (10 × 10)

Type below:
__________

Explanation:
1 roll = 50 dimes ;
Think:50 dimes per roll × 20 rolls =(5 × 2) × (10 × 10) = 10 x 102
50 dimes per roll × 30 rolls = (5 x 3) x (10 × 10) = 15 x 102
50 dimes per roll × 40 rolls = (5 x 4) x (20 × 10) = 20 x 102
50 dimes per roll × 50 rolls = (5 x 5) x (10 × 10) = 25 x 102
50 dimes per roll × 60 rolls = (5 x 6) x (10 × 10) = 30 x 102
50 dimes per roll × 70 rolls = (5 x 7) x (10 × 10) = 35 x 102
50 dimes per roll × 80 rolls = (5 x 8) x (10 × 10) = 40 x 102
50 dimes per roll × 90 rolls = (5 x 9) x (10 × 10) = 45 x 102
50 dimes per roll × 100 rolls = (5 x 10) x (10 × 10) = 50 x 102

Question 21.
1 roll = 40 quarters ; Think:40 quarters per roll × 20 rolls =(4 × 2) × (10 × 10)

Type below:
__________

Explanation:
1 roll = 40 quarters ;
Think:40 quarters per roll × 20 rolls =(4 × 2) × (10 × 10) = 8 x 102
40 quarters per roll × 30 rolls =(4 × 3) × (10 × 10) = 12 x 102
40 quarters per roll × 40 rolls =(4 × 4) × (10 × 10) = 16 x 102
40 quarters per roll × 50 rolls =(4 × 5) × (10 × 10) = 20 x 102
40 quarters per roll × 60 rolls =(4 × 6) × (10 × 10) = 24 x 102
40 quarters per roll × 70 rolls =(4 × 7) × (10 × 10) = 28 x 102
40 quarters per roll × 80 rolls =(4 × 8) × (10 × 10) = 32 x 102
40 quarters per roll × 90 rolls =(4 × 9) × (10 × 10) = 36 x 102
40 quarters per roll × 100 rolls =(4 × 10) × (10 × 10) = 40 x 102

Question 22.

Type below:
__________

Explanation:
80 x 800 = 64 x 103
80 x 6 = (8 x 6) x 10 = 48 x 101
80 x 70 = (8 x 7) x (10 x 10) = 56 x 102
80 x 9,000 = (8 x 9) x (10 x 10 x 10 x 10) = 64 x 104

Question 23.

Type below:
__________

Explanation:
Given that
90 x 9,000 = (9 x 9) x 10 x 10 x 10 x 10 = 81 x 104
90 x 6 = (9 x 6) x 10 = 54 x 101
90 x 70 = (9 x 7) x (10 x 10) = 63 x 102
90 x 800 = (9 x 8) x (10 x 10 x 10) = 72 x 103

Problem Solving

Use the table for 24–26.

Question 24.
What if you magnified the image of a cluster fly by 9 × 103 ? What would the length appear to be?

____ mm

9,000 mm

Explanation:
9 × 103  = 9 x 10 x 10 x 10 = 9,000

Question 26.
John wants to magnify the image of a fire ant and a crab spider so they appear to be the same length. How many times their actual sizes would he need to magnify each image?
Fire ant by _______ times
Crab spider by ______ times

Fire ant by 5 times
Crab spider by 4 times

Explanation:
Given that Fire ant = 4 mm
crab spider = 5 mm
So, to make them have the same lengths, multiply fire ant by 5 mm and multiply Crab spider by 4 mm

### Multiplication Patterns – Share and Show – Page No. 24

Question 27.
What does the product of any whole-number factor multiplied by 100 always have? Explain.
Type below:
__________

The product of any whole number factor multiplied by 100 has two digits which are 0 in ones and tens places.
Example: 2 x 100 = 200

Question 28.
Test Prep How many zeros are in the product (5 × 4) × 104?
Options:
A. 3
B. 4
C. 5
D. 6

C. 5

Explanation:
(5 × 4) × 104 = 20 x 104 = 2 x 105
5 zeroes

Use patterns and mental math to solve.

Question 31.
Lymphocytes and eosinophils are types of white blood cells. A blood sample has about 10 times as many lymphocytes as eosinophils. If there are 2 × 102 eosinophils in the sample, about how many lymphocytes are there?
______ lymphocytes

2 × 103 lymphocytes

Explanation:
Lymphocytes and eosinophils are types of white blood cells. A blood sample has about 10 times as many lymphocytes as eosinophils.
There are 2 × 102 eosinophils in the sample
Then, Lymphocytes = 10 x 2 × 102 eosinophils = 2 × 103

Question 32.
An average person has 6 × 102 times as many red bloods cells as white blood cells. A small sample of blood has 7 × 103 white blood cells. About how many red blood cells are in the sample?
______ red blood cells

42 x 10 red blood cells

Explanation:
Let the red blood cells = S
S = 7 × 103 x 6 × 102
S = 42 x 10

### Mid-Chapter Checkpoint – Vocabulary – Page No. 25

Choose the best term for the box.

Question 1.
A group of three digits separated by commas in a multidigit number is a __
________

Period

Question 2.
An __ is the number that tells how many times a base is used as a factor
________

exponent

Concepts and Skills

Complete the sentence.

Question 3.
7 is $$\frac{1}{10}$$ of ______

70

Explanation:
Let the unknown number is S.
7 = $$\frac{1}{10}$$ S
S = 7 X 10 = 70

Question 4.
800 is 10 times as much as ______

80

Explanation:
Let the unknown number is S.
800 = 10S
S = 800/10 = 80.

Write the value of the underlined digit.

Question 5.
6,581,678
________

80,000

Explanation:
(6 x 1,000,000) + (5 x 1,00,000) + (8 x 10,000) + (1 x 1,000) + (6 x 100) + (7 x 10) + (8 x 1)
8 x 10,000 = 80,000

Question 6.
25,634
________

600

Explanation:
(2 x 10,000) + (5 x 1,000) + (6 x 100) + (3 x 10) + (4 x 1)
6 x 100 = 600

Question 7.
34,634,803
________

4,000,000

Explanation:
(3 x 10,000,000) + (4 x 1,000,000) + (6 x 1,00,000) + (3 x 10,000) + (4 x 1,000) + (8 x 100) + (0 x 10) + (3 x 1)
4 x 1,000,000 = 4,000,000

Question 8.
2,764,835
________

700,000

Explanation:
(2 x 1,000,000) + (7 x 1,00,000) + (6 x 10,000) + (4 x 1,000) + (8 x 100) + (3 x 10) + (5 x 1)
7 x 1,00,000 = 700,000

Complete the equation, and tell which property you used.

Question 9.
8 × (14 + 7) = ________ + (8 × 7)

8 × (14 + 7) = (8 x 14) + (8 × 7);
Distributive Property of Multiplication

Explanation:
8 × (14 + 7)
(8 x 14) + (8 × 7); Distributive Property of Multiplication

Question 10.
7 + (8 + 12) = ________ + 12

7 + (8 + 12) = (7 + 8) + 12

Find the value.

Question 11.
103 = ______

1,000

Explanation:
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;

Question 12.
6 × 102 = ______

600

Explanation:
6 × 102
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
6 x 100 = 600

Question 13.
4 × 104 = ______

40,000

Explanation:
4 × 104
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
4 x 10,000 = 40,000

Use mental math and a pattern to find the product.

Question 14.
70 × 300 = ______

21,000

Explanation:
70 × 300 = (7 x 3) x (10 x 10 x 10) = 21 x 1,000 = 21,000

Question 15.
(3 × 4) × 103 = ______

12,000

Explanation:
(3 × 4) × 103
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
12 x 1,000 = 12,000

Question 16.
DVDs are on sale for $24 each. Which expression can be used to find the cost in dollars of buying 4 DVDs? Options: A. (4 + 20) + (4 + 4) B. (4 × 20) + (4 × 4) C (4 + 20) × (4 + 4) D. (4 × 20) × (4 × 4) Answer: B. (4 × 20) + (4 × 4) Explanation: 24 can be written as 25 – 1 4 x 24 = 4 x (20 + 4) = (4 x 20) + (4 x 4) Question 17. The Muffin Shop chain of bakeries sold 745,305 muffins last year. Which choice shows that number in expanded form? Options: A. (7 × 100,000) + (45 × 10,000) + (3 × 100) + (5 × 10) B. (7 × 100,000) + (4 × 10,000) + (5 × 1,000) + (5 × 10) C. (7 × 100,000) + (4 × 10,000) + (5 × 1,000) + (3 × 100) + (5 × 1) D. (7 × 100,000) + (4 × 10,000) + (3 × 100) + (5 × 1) Answer: C. (7 × 100,000) + (4 × 10,000) + (5 × 1,000) + (3 × 100) + (5 × 1) Explanation: First, we can write 745,305 as: 700,000 + 40, 000 + 5,000 + 300 + 5 (7 x 100,000) + (4 x 10,000) + (5 x 1,000) + (3 x 100) + 5 Question 18. The soccer field at Mario’s school has an area of 6,000 square meters. How can Mario show the area as a whole number multiplied by a power of ten? Options: A. 6 × 104 sq m B. 6 × 103 sq m C. 6 × 102 sq m D. 6 × 101 sq m Answer: B. 6 × 103 sq m Explanation: 6,000 square meters = 6 x 1,000 = 6 x 10 x 10 x 10 = 6 × 103 sq m Question 19. Ms. Alonzo ordered 4,000 markers for her store. Only $$\frac{1}{10}$$ of them arrived. How many markers did she receive? Options: A. 4 B. 40 C. 400 D. 1,400 Answer: C. 400 Explanation: Ms. Alonzo ordered 4,000 markers for her store. Only $$\frac{1}{10}$$ of them arrived. 4,000 x $$\frac{1}{10}$$ = 400 Question 20. Mark wrote the highest score he made on his new video game as the product of 70 × 6,000. What was his score? Options: A. 420 B. 4,200 C. 42,000 D. 420,000 Answer: D. 420,000 Explanation: Mark wrote the highest score he made on his new video game as the product of 70 × 6,000. (7 x 6) x (10 x 10 x 10 x 10) = 42 x 10,000 = 420,000 ### Multiply by 1-digit numbers – Share and Show – Page No. 29 Complete to find the product. Question 1. 6 × 796 Estimate: 6 × ___ = ___ ______ Answer: 4,776 Explanation: Estimate. Then find the product. Question 2. Estimate: ___ 6 0 8 × 8 ———- Estimate: ________ Product: 608 × 8 = ________ Answer: Estimate: 6,000 Product: 608 × 8 = 4,864 Explanation: Estimate: 608 is close to 600; 8 is close to 10 600 x 10 = 6,000 608 x 8 Multiply the ones; 8 x 8 = 64. 4 ones and 6 tens. Write the ones and the regrouped tens. Multiply the tens; 0 x 8 = 0 + 6 = 6 Multiply the hundreds; 6 x 8 = 48. So, 4,864 is the product of 608 × 8 Product: 4,864 Question 4. Estimate: 1,925 × 7 ———– Estimate: ________ Product: 1,925 × 7 = ________ Answer: Estimate: 10,000 Product: 1,925 × 7 = 13,475 Explanation: Estimate: 1,925 is close to 2000; 7 is close to 5 2,000 x 5 = 10,000 1,925 × 7 Multiply the ones; 7 x 5 = 35. 5 ones and 3 tens. Write the ones and the regrouped tens. Multiply the tens; 7 x 2 = 14; 14 + 3 = 17; 7 tens and 1 hundreds. Write the tens and regrouped hundreds. Multiply the hundreds; 7 x 9 = 63; 63 + 1 = 64. 4 hundred and 6 thousand Write the hundreds and regrouped thousands. Multiply the thousands; 7 x 1 = 7; 7 + 6 = 13 So, 13,475 is the product of 1,925 × 7 Product: 13,475 On Your Own Estimate. Then find the product. Question 5. Estimate:__ 7 9 4 × 3 ———- Estimate: ________ Product:794 × 3 = ________ Answer: Estimate: 800 Product:794 × 3 = 2,382 Explanation: Estimate: 794 is close to 800 and 3 is close to 1 800 x 1 = 800 794 x 3 = (700 + 90 + 4) x 3 = (700 x 3) + (90 x 3) + (4 x 3) = 2100 + 270 + 12 = 2,382 Question 7. Estimate: 3,102 × 5 ———– Estimate: ________ Product: 3,102 × 5 = ________ Answer: Estimate: 15,500 Product: 3,102 × 5 = 15,510 Explanation: Estimate: 3,102 is close to 3,100 and 5 is close to 5 3,100 x 5 = 15,500 3,102 x 5 = (3,000 + 100 + 0 + 2) x 5 = (3000 x 5) + (100 x 5) + 0 + (2 x 5) = 15,000 + 500 + 0 + 10 = 15,510 Algebra Solve for the unknown number. Question 8. 3 9 6 × 6 ——— 2, 3 6 396 × 6 = 23 ______ 6 Answer: 7 Explanation: 396 x 6 = (300 + 90 + 6) x 6 = (300 x 6) + (90 x 6) + (6 x 6) = 1800 + 540 + 36 = 2376. So, the unknown number is 7 Question 9. 5,1 2 × 8 ——– 16 Type below: __________ Answer: 5127 x 8 = 41,016. Unknown numbers = 7 and 410 Explanation: 5,127 x 8 = (5000 + 100 + 20 + 7) x 8 = (5000 x 8) + (100 x 8) + (20 x 8) + (7 x 8) = 40000 + 800 + 160 + 56 = 41,016 Question 10. 8, 5 6 × 7 ——— 60,03 Type below: __________ Answer: 8,576 x 7 = 60,032 Explanation: 8,576 x 7 = (8000 + 500 + 70 + 6) x 7 = (8000 x 7) + (500 x 7) + (70 x 7) + (6 x 7) = 56000 + 3500 + 490 + 42 = 60,032 Practice: Copy and Solve Estimate. Then find the product. Question 11. 116 × 3 = _______ Estimate: _______ Answer: Estimate: 300 116 × 3 = 348 Explanation: Estimate: 116 is close to 100; 100 x 3 = 300 116 x 3 6 x 3 =18; add ones and regroup tens 3 x 1 = 3; 3 + 1 = 4 3 x 1 = 3 So, 348 is the product Question 12. 338 × 4 = _______ Estimate: _______ Answer: 338 × 4 = 1,352 Estimate: 1,200 Explanation: Estimate: 338 is close to 300; 300 x 4 = 1,200 338 × 4 8 x 4 =32; add ones and regroup tens 3 x 4 = 12; 12 + 3 = 15; add tens and regroup hundreds 3 x 4 = 12; 12 + 1 = 13 So, 1352 is the product Question 13. 6 × 219 = _______ Estimate: _______ Answer: 6 × 219 = 1,314 Estimate: 1200 Explanation: Estimate: 219 is close to 200 200 x 6 = 1200 6 × 219 6 x 9 = 54; add ones and regroup tens 6 x 1 = 6; 6 + 5 = 11; add tens and regroup hundreds 6 x 2 = 12; 12 + 1 = 13 So, 1,314 Question 14. 7 × 456 = _______ Estimate: _______ Answer: 7 × 456 = 3192 Estimate: 3500 Explanation: Estimate: 456 is close to 500 500 x 7 = 3500 7 x 456 7 x 6 = 42; add ones and regroup tens 7 x 5 = 35; 35 + 4 = 39; add tens and regroup hundreds 7 x 4 = 28; 28 + 3 = 31 So, 3192 Question 15. 5 × 1,012 = _______ Estimate: _______ Answer: 5 × 1,012 = 5,060 Estimate: 5,000 Explanation: Estimate: 1,012 is close to 1,000 1,000 x 5 = 5,000 5 × 1,012 5 x 2 = 10; add ones and regroup tens 5 x 1 = 5; 5 + 1 = 6; add tens and regroup hundreds 5 x 0 = 0 5 x 1 = 5 So, 5,060 Question 16. 2,921 × 3 = _______ Estimate: _______ Answer: 2,921 × 3 = 8,763 Estimate: 9,000 Explanation: Estimate: 2,921 is close to 3,000 3,000 x 3 = 9,000 2,921 × 3 3 x 1 = 3; 3 x 2 = 6; 3 x 9 = 27; add hundreds and regroup thousands 3 x 2 = 6; 6 + 2 = 8 So, 8,763 Question 18. 9 × 3,033 = _______ Estimate: _______ Answer: Explanation: Estimate: 3,033 is close to 3,000 3,000 x 9 = 27,000 9 × 3,033 9 x 3 = 27; add ones and regroup tens 9 x 3 = 27; 27 + = 11; add tens and regroup hundreds 6 x 2 = 12; 12 + 1 = 13 So, 1,314 ### Multiply by 1-digit numbers – Problem Solving – Page No. 30 What’s the Error? Question 19. The Plattsville Glee Club is sending 8 of its members to a singing contest in Cincinnati, Ohio. The cost will be$588 per person. How much will it cost for the entire group of 8 students to attend? Both Brian and Jermaine solve the problem. Brian says the answer is $40,074. Jermaine’s answer is$4,604.
Estimate the cost. A reasonable estimate is _
$______ Answer:$4,800

Explanation:
The Plattsville Glee Club is sending 8 of its members to a singing contest in Cincinnati, Ohio. The cost will be $588 per person. So, for entire group 8 x$588 = $4,704 Jermaine’s answer is correct. Because the$4,604 is close to $4,704 588 is close to 600. So, 600 x 8 =$4,800

Question 19.
Although Jermaine’s answer seems reasonable, neither Brian nor Jermaine solved the problem correctly. Find the errors in Brian’s and Jermaine’s work.
Then, solve the problem correctly.

What error did Brian make? Explain.
Type below:
__________

When Brian multiplied the tens, he wrote the total number of tens in the product instead of regrouping, so the place values of his product are incorrect.

Question 19.
What error did Jermaine make? Explain.
Type below:
__________

Jermaine regrouped the wrong amount of hundreds. He regrouped the tens as 6 hundred instead of 7 hundred.
$588 x 8 =$4,704

Question 19.
How could you predict that Jermaine’s answer might be incorrect using your estimate?
Type below:
__________

I used 600 × 8 to estimate the product; 588 is 12 less than 600. Since 12 × 8 = 96, and 4,604 is almost 200 less than the estimate of 4,800, the answer is probably too low.

### Multiply by 2-digit numbers – Share and Show – Page No. 33

Complete to find the product

Question 1.

Type below:
__________

2,752

Explanation:
64 x 3 = 192
64 x 40 = 2,560
2,560 + 192 = 2,752

Question 2.

Type below:
__________

21,698

Explanation:
571 x 8 = 4,568
571 x 30 = 17,130
17,130 + 4,568 = 21,698

Estimate. Then find the product.

Question 3.
Estimate:____
2 4
× 1 5
———-
Estimate: ________
Product: ________

Estimate: 300
Product: 360

Explanation:
2 4 x 15
Estimate: 20 x 15 = 300
24 x 5 = 120
24 x 10 = 240
Product:: 240 + 120 = 360

Estimate. Then find the product.

Question 6.
Estimate:____
2 8
× 2 2
———-
Estimate: ________
Product: ________

Estimate: 600
Product: 616

Explanation:
28 x 22
Estimate: 30 x 20 = 600
28 x 2 = 56
28 x 20 = 560
Product:: 56 + 560 = 616

Question 7.
Estimate:____
9 3
× 7 6
———-
Estimate: ________
Product: ________

Estimate: 7200
Product: 7,068

Explanation:
93 x 76
Estimate: 90 x 80 = 7200
93 x 6 = 558
93 x 70 = 6,510
Product:: 558 + 6,510 = 7,068

Question 8.
Estimate:____
2 9 5
× 5 1
———-
Estimate: ________
Product: ________

Estimate: 15,000
Product: 15,045

Explanation:
295 x 51
Estimate: 300 x 50 = 15,000
295 x 1 = 295
295 x 50 = 14,750
Product:: 295 + 14,750 = 15,045

Practice: Copy and Solve Estimate. Then find the product.

Question 9.
Estimate: ________
54 × 31 = ________

Estimate: 1,500
Product: 1,674

Explanation:
54 x 31
Estimate: 50 x 30 = 1,500
54 x 1 = 54
54 x 30 = 1,620
Product:: 54 + 1,620 = 1,674

Question 10.
Estimate: ________
42 × 26 = ________

Estimate: 1,200
Product: 1,092

Explanation:
42 x 26
Estimate: 40 x 30 = 1,200
42 x 6 = 252
42 x 20 = 840
Product:: 252 + 840 = 1,092

Question 11.
Estimate: ________
38 × 64 = ________

Estimate: 2,400
Product: 2,432

Explanation:
38 × 64
Estimate: 40 x 60 = 2,400
38 x 4 = 152
38 x 60 = 2,280
Product:: 152 + 2,280 = 2,432

Question 12.
Estimate: ________
63 × 16 = ________

Estimate: 1,200
Product: 1,008

Explanation:
63 x 16
Estimate: 60 x 20 = 1,200
63 x 6 = 378
63 x 10 = 630
Product:: 378 + 630 = 1,008

Question 13.
Estimate: ________
204 × 41 = ________

Estimate: 8,000
Product: 8,364

Explanation:
204 × 41
Estimate: 200 x 40 = 8,000
204 x 1 = 204
204 x 40 = 8,160
Product:: 204 + 8,160 = 8,364

Question 14.
Estimate: ________
534 × 25 = ________

Estimate: 15,000
Product: 13,350

Explanation:
534 x 25
Estimate: 500 x 30 = 15,000
534 x 5 = 2,670
534 x 20 = 10,680
Product:: 2,670 + 10,680 = 13,350

Question 15.
Estimate: ________
722 × 39 = ________

Estimate: 28,000
Product: 28,158

Explanation:
722 × 39
Estimate: 700 x 40 = 28,000
722 x 9 = 6,498
722 x 30 = 21,660
Product:: 6,498 + 21,660 = 28,158

Question 16.
Estimate: ________
957 × 43 = ________

Estimate: 40,000
Product: 44,022

Explanation:
957 × 43
Estimate: 1,000 x 40 = 40,000
957 x 3 = 2,871
957 x 40 = 41,151
Product:: 2,871 + 41,151 = 44,022

### Multiply by 2-digit numbers – Problem Solving – Page No. 34

Use the table for 17–20.

Question 17.
How much sleep does a jaguar get in 1 year?

_____ hours

4,004 hours

Explanation:
52 weeks x 77 = 4,004 hours

Question 18.
In 1 year, how many more hours of sleep does a giant armadillo get than a platypus?
_____ hours

1,508 hours

Explanation:
giant armadillo: 52 x 127 = 6,604
platypus: 52 x 98 = 5,096
6,604 – 5,096 = 1,508

Question 19.
Owl monkeys sleep during the day, waking about 15 minutes after sundown to find food. At midnight, they rest for an hour or two, then continue to feed until sunrise. They live about 27 years. How many hours of sleep does an owl monkey that lives 27 years get in its lifetime?
_____

4927.5 days

Explanation:
Given that the time of Owl monkeys sleeps during the day walking about 15 minutes after sundown. Then, at midnight they rest for an hour or two then continue to feed until sunrise. Notice that the above description doesn’t say that they sleep in after sundown. They either eat or rest.
Day time is usually considered from 6 am to 6 pm which is total of 12 hours.
As per the given information, owl monkey sleeps in that period.
Given that owl, monkeys live for 27 years.
So the time for sleeping in their lifetime = 12 hours * 27 years
= (12/24 days) * 27 years
= (1/2 days) * 27 years
= (1/2 days) * (27*365 days)
= (1/2 days) * (9855 days)
= 4927.5 days
Hence final answer is 4927.5 days.

Question 20.
Three-toed sloths move very slowly, using as little energy as possible. They sleep, eat, and even give birth upside down. A baby sloth may cling to its mother for as much as 36 weeks after being born. How much of that time is the sloth asleep?
_____ hours

3,636 hours

Explanation:
101 x 36 = 3,636

Question 21.
Test Prep A sloth’s maximum speed on the ground is 15 feet in 1 minute. Even though it would be unlikely for a sloth to stay in motion for more than a few moments, how far would a sloth travel in 45 minutes at that speed?
Options:
A. 60 feet
B. 270 feet
C. 675 feet
D. 6,750 feet

C. 675 feet

Explanation:
sloth’s maximum speed on the ground is 15 feet in 1 minute. For 45 minutes, 45 x 15 = 675 feet

### Relate Multiplication to Division – Share and Show – Page No. 37

Question 1.
Brad has 72 toy cars that he puts into 4 equal groups. How many cars does Brad have in each group? Use the array to show your answer.
4 × = 72         72 ÷ 4 =

4 × ________ = 72
72 ÷ 4 = ________

Explanation:
Brad has 18 toy cars in each group.
Because 72÷4 =18
4 × 18 = 72
4 x (9 + 9) = (4 x 9) + (4 x 9)

Use multiplication and the Distributive Property to find the quotient.

Question 2.
108 ÷ 6 = _____

18

Explanation:
108 ÷ 6
6 x 18 = 6 x (9 + 9) = (6 x 9) + (6 x 9) = 54 + 54 = 108
(36 + 72) ÷ 6 = (36 ÷ 6) + (72÷ 6) = 6 + 12 = 18

Use multiplication and the Distributive Property to find the quotient.

Question 5.
60 ÷ 4 = _____

15

Explanation:
60 ÷ 4
(20 + 40) ÷ 4 = (20 ÷ 4) + (40 ÷ 4) = 5 + 10 = 15
4 x 15 = 4 x (7+ 8) = (4 x 7) + (4 x 8) = 28 + 32 = 60

Question 6.
144 ÷ 6 = _____

24

Explanation:
144 ÷ 6
(72 + 72) ÷ 6 = (72 ÷ 6) + (72 ÷ 6) = 12 + 12 = 24
6 x 24 = 6 x ( 12 + 12) = (6 x 12) + (6 x 12) = 72 + 72 = 144

Question 7.
252 ÷ 9 = _____

28

Explanation:
252 ÷ 9
(126 + 126) ÷ 9 = (126 ÷ 9) + (126 ÷ 9) = 14 + 14 = 28
6 x 28 = 6 x ( 14 + 14) = (6 x 14) + (6 x 14) = 126 + 126 = 252

Find each quotient. Then compare. Write <, > or =.

Question 8.
51 ÷ 3 _____ 68 ÷ 4

51 ÷ 3 = 68 ÷ 4

Explanation:
51 ÷ 3 = 17
68 ÷ 4 = 17
17 = 17.

Question 9.
252 ÷ 6 _____ 135 ÷ 3

252 ÷ 6 < 135 ÷ 3

Explanation:
252 ÷ 6 = 42
135 ÷ 3 = 45
42 < 45

Question 10.
110 ÷ 5 _____ 133 ÷ 7

110 ÷ 5 > 133 ÷ 7

Explanation:
110 ÷ 5 = 22
133 ÷ 7 = 19
22 > 19

### Relate Multiplication to Division – Problem Solving – Page No. 38

Use the table to solve 11–13.

Question 11.
A group of 6 friends share a bag of the 45-millimeter bouncy balls equally among them. How many does each friend get?

____ balls

7 balls

Explanation:
A group of 6 friends shares a bag of the 45-millimeter bouncy balls equally among them.
45/6 = 7 balls and 3 balls remained

Question 12.
Mr. Henderson has 2 bouncy-ball vending machines. He buys one bag of the 27-millimeter balls and one bag of the 40-millimeter balls. He puts an equal number of each in the 2 machines. How many bouncy balls does he put in each machine?
________ balls of the 27-millimeter .
________ balls of the 40-millimeter .
________ total balls

51 balls of the 27-millimeter
29 balls of the 40-millimeter
80 total balls

Explanation:
There’s 51 27 mm, 29 40 mm

Question 13.
Lindsey buys a bag of each size of bouncy ball. She wants to put the same number of each size of bouncy ball into 5 party-favor bags. How many of each size of bouncy ball will she put in a bag?
________ balls of the 27-millimeter
________ balls of the 40-millimeter
________ balls of the 45-millimeter

34 balls of the 27-millimeter
12 balls of the 40-millimeter
34 balls of the 45-millimeter

Explanation:
There’s 34 27 mm, 12 40 mm, and 34 45 mm bouncy balls

Question 15.
Test Prep Which of the following can be used to find 150 ÷ 6?
Options:
A. (6 × 20) + (6 × 5)
B. (6 × 10) + (6 × 5)
C. (2 × 75) + (2 × 3)
D. (6 × 15) + (6 × 5)

A. (6 × 20) + (6 × 5)

Explanation:
150 ÷ 6 = 25
25 x 6 = 150
6 x 25 = 6 x (20 + 5) = (6 × 20) + (6 × 5)

### Problem Solving Multiplication and Division – Share and Show – Page No. 41

Question 1.
To make concrete mix, Monica pours 34 pounds of cement, 68 pounds of sand, 14 pounds of small pebbles, and 19 pounds of large pebbles into a large wheelbarrow. If she pours the mixture into 9 equalsize bags, how much will each bag weigh?
First, find the total weight of the mixture.
____ pounds

135 pounds

Explanation:
34 + 68 + 14 + 19 = 135

Question 1.
Then, divide the total by the number of bags. Break the total into two simpler numbers to make the division easier, if necessary.
Finally, find the quotient and solve the problem.
So, each bag will weigh _ pounds.
____ pounds

15 pounds

Explanation:
now, calculate 135/9 = 15 pounds.

Question 2.
What if Monica pours the mixture into 5 equal-size bags? How much will each bag weigh?
____ pounds

27 pounds

Explanation:
135/5 = 27

Question 3.
Taylor is building doghouses to sell. Each doghouse requires 3 full sheets of plywood which Taylor cuts into new shapes. The plywood is shipped in bundles of 14 full sheets. How many doghouses can Taylor make from 12 bundles of plywood?
____

56 doghouses

Explanation:
Taylor is building doghouses to sell. Each doghouse requires 3 full sheets of plywood which Taylor cuts into new shapes. The plywood is shipped in bundles of 14 full sheets.
(12 x 14)/3 = 168/3 = 56 doghouses

Question 4.
Eileen is planting a garden. She has seeds for 60 tomato plants, 55 sweet corn plants, and 21 cucumber plants. She plants them in 8 rows, with the same number of plants in each row. How many seeds are planted in each row?
____ seeds / row

17 seeds

Explanation:
Eileen is planting a garden. She has seeds for 60 tomato plants, 55 sweet corn plants, and 21 cucumber plants. She plants them in 8 rows, with the same number of plants in each row.
60 + 55 + 21 = 136
136/8 = 17

### Problem Solving Multiplication and Division – On Your Own – Page No. 42

Question 5.
Starting on day 1 with 1 jumping jack, Keith doubles the number of jumping jacks he does every day. How many jumping jacks will Keith do on day 10?
____  jumping jack

512 jumping jacks

Explanation:
She doubled the number so you’re supposed to multiply by 2.
On day 1, 1 jumping pack;
On day 2, 2 jumping packs;
On day 3, 2 x 2 = 4 jumping packs;
On day 4, 2 x 2 x 2 = 8 jumping packs;
On day 5, 2 x 2 x 2 x 2 = 16 jumping packs;
On day 6, 2 x 2 x 2 x 2 x 2 = 32 jumping packs;
On day 7, 2 x 2 x 2 x 2 x 2 x 2 = 64 jumping packs;
On day 8, 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128 jumping packs;
On day 9, 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 jumping packs;
On day 10, 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512 jumping packs;
512 jumping jacks

Question 6.
Starting in the blue square, in how many different ways can you draw a line that passes through every square without picking up your pencil or crossing a line you’ve already drawn? Show the ways.

____ ways

8 ways

Explanation:

8 ways

Question 7.
On April 11, Millie bought a lawn mower with a 50-day guarantee. If the guarantee begins on the date of purchase, what is the first day on which the mower will no longer be guaranteed?
__________

May 31

Explanation:
The guarantee begins on April 11. April has 30 days. So, we have 20 days of the guarantee in April.
May has 31 days. So, we have 30 days of the guarantee in May.
Therefore, the last day of the guarantee is May 31.

Question 10.
Test Prep Dee has 112 minutes of recording time. How many 4-minute songs can she record?
Options:
A. 28
B. 27
C. 18
D. 17

A. 28

Explanation:
Dee has 112 minutes of recording time. 112/4 = 28

### Numerical Expressions – Share and Show – Page No. 45

Circle the expression that matches the words.

Question 1.
Teri had 18 worms. She gave 4 worms to Susie and 3 worms to Jamie.
(18 – 4) + 3         18 – (4 + 3)
__________

18 – (4 + 3)

Explanation:
Teri had 18 worms. She gave 4 worms.
18 – 4 = 14.
3 worms to Jamie
14 – 3 = 11.
(18 – 4) + 3 = 14 + 3 = 17 not equal to 11;
18 – (4 + 3) = 18 – 7 = 11 = 11

Question 2.
Rick had $8. He then worked 4 hours for$5 each hour.
$8 + (4 ×$5)       ($8 + 4) ×$5
__________

$8 + (4 ×$5)

Explanation:
Rick had $8. He then worked 4 hours for$5 each hour = 4 x $5 =$20;
$20 +$8 =$28.$8 + (4 × $5) = 8 + 20 =$28 = $28. Write an expression to match the words. Question 4. Lynda has 27 fewer fish than Jack. Jack has 80 fish. Type below: __________ Answer: 80 – 27 = 53 Explanation: Lynda has 27 fewer fish than Jack. Jack has 80 fish. 80 – 27 = 53 Write words to match the expression. Question 5. 34 – 17 Type below: __________ Answer: Anna has 17 fewer apples than Jack. Jack has 34 apples. Explanation: 34 – 17 = 17. Anna has 17 fewer apples than Jack. Jack has 34 apples. Question 6. 6 × (12 – 4) Type below: __________ Answer: Teri had 12 worms. She gave 4 worms to Susie. She sell remaining worms for$6 each.

Explanation:
Teri had 12 worms. She gave 4 worms to Susie. She sell remaining worms for $6 each. On Your Own Write an expression to match the words. Question 7. José shared 12 party favors equally among 6 friends. Type below: __________ Answer: 12/6 = 2 Explanation: José shared 12 party favors equally among 6 friends. 12/6 = 2 Question 8. Braden has 14 baseball cards. He finds 5 more baseball cards. Type below: __________ Answer: 14 + 5 = 19 Explanation: Braden has 14 baseball cards. He finds 5 more baseball cards. 14 + 5 = 19 Question 9. Isabelle bought 12 bottles of water at$2 each.
Type below:
__________

12 x $2 =$24

Explanation:
Isabelle bought 12 bottles of water at $2 each. 12 x$2 = $24 Question 10. Monique had$20. She spent $5 on lunch and$10 at the bookstore.
Type below:
__________

20 – (5 + 10)

Explanation:
Monique had $20. She spent$5 on lunch and $10 at the bookstore. 20 – (5 + 10) Write words to match the expression. Question 11. 36 ÷ 9 Type below: __________ Answer: Anna shared 36 apples to 9 friends. Question 12. 35 – (16 + 11) Type below: __________ Answer: Monique had 35 balls. She gave 16 to her one frined and 11 to other friend. Draw a line to match the expression with the words. Question 13. Fred catches 25 fish. Then he releases 10 fish and catches 8 more. • •3 × (15 – 6) Nick has 25 pens. He gives 10 pens to one friend and 8 pens to another friend. • •15 – 6 Jan catches 15 fish and lets 6 fish go. • •25 – (10 + 8) Libby catches 15 fish and lets 6 fish go for three days in a row. • •(25 – 10) + 8 Type below: __________ Answer: Fred catches 25 fish. Then he releases 10 fish and catches 8 more = (25 – 10) + 8 Nick has 25 pens. He gives 10 pens to one friend and 8 pens to another friend = 25 – (10 + 8) Jan catches 15 fish and lets 6 fish go = 15 – 6 Libby catches 15 fish and lets 6 fish go for three days in a row = 3 × (15 – 6) ### Numerical Expressions – Problem Solving – Page No. 46 Use the rule and the table for 14. Question 14. Write a numerical expression to represent the total number of lemon tetras that could be in a 20-gallon aquarium. _____ lemon tetras Answer: 2 lemon tetras Explanation: From the given data, increase each inch of lenth, 1 gallon of water increases. 2 + 3 + 5 + 3 + 5 = 18 inches. So, 18 gallon of water available in aquarium. Add 1 lemon tetra to get the 20 gallon of water. So, in total there are 2 lemon tetra available. Question 15. Write a word problem for an expression that is three times as great as (15 + 7). Then write the expression. Type below: __________ Answer: 3 x (15 + 7) Explanation: Given that that is three times as great as (15 + 7) Question 16. What’s the Question? Lu has 3 swordtails in her aquarium. She buys 2 more swordtails. Type below: __________ Answer: 3 + 2 = 5 Explanation: Lu has 3 swordtails in her aquarium. She buys 2 more swordtails. So, 3 + 2 = 5 swordtails Question 17. Tammy gives 45 stamps to her 9 friends. She shares them equally among her friends. Write an expression to match the words. How many stamps does each friend get? _____ stamps Answer: 45/9 = 5 stamps Explanation: Tammy gives 45 stamps to her 9 friends. 45/9 = 5. Question 18. Test Prep Josh has 3 fish in each of 5 buckets. Then he releases 4 fish. Which expression matches the words? Options: a. (3 × 4) – 5 b. (5 × 4) – 3 c. (5 × 3) – 4 d. (5 – 3) × 4 Answer: c. (5 × 3) – 4 Explanation: Josh has 3 fish in each of 5 buckets. 3 x 5. Then he releases 4 fish. (3 x 5) – 4 ### Evaluate Numerical Expressions – Share and Show – Page No. 49 Evaluate the numerical expression. Question 1. 10 + 36 ÷ 9 _____ Answer: 14 Explanation: 10 + 36 ÷ 9 = 10 + (36 ÷ 9) = 10 + 4 = 14 Question 2. 10 + (25 – 10) ÷ 5 _____ Answer: 13 Explanation: 10 + (25 – 10) ÷ 5 = 10 + 15 ÷ 5 = 10 + (15 ÷ 5) = 10 + 3 = 13 Question 3. 9 – (3 × 2) + 8 _____ Answer: 11 Explanation: 9 – (3 × 2) + 8 = 9 – 6 + 8 = 3 + 8 = 11 On Your Own Evaluate the numerical expression. Question 6. 36 – (8 + 5) _____ Answer: 23 Explanation: 36 – (8 + 5) = 36 – 13 = 23 Question 7. 125 – (68 + 7) _____ Answer: 50 Explanation: 125 – (68 + 7) = 125 – 75 = 50 Question 8. (4 × 6) – 12 _____ Answer: 12 Explanation: (4 × 6) – 12 = 24 – 12 = 12 Question 9. 3 × (22 – 2) _____ Answer: 60 Explanation: 3 × (22 – 2) = 3 x 20 = 60 Question 10. 23 + (16 – 7) _____ Answer: 32 Explanation: 23 + (16 – 7) = 23 + 9 = 32 Question 11. (25 – 4) ÷ 3 _____ Answer: 7 Explanation: (25 – 4) ÷ 3 = 21 ÷ 3 = 7 Rewrite the expression with parentheses to equal the given value. Question 12. 100 – 30 ÷ 5 value: 14 Type below: __________ Answer: (100 – 30) ÷ 5 = 14 Explanation: 100 – 30 ÷ 5 = (100 – 30) ÷ 5 = 70 ÷ 5 = 14 Question 13. 12 + 17 – 3 × 2 value: 23 Type below: __________ Answer: 23 Explanation: (12 + 17) – (3 × 2) = 29 – 6 = 23 Question 14. 9 + 5 ÷ 5 + 2 value: 12 Type below: __________ Answer: 12 Explanation: 9 + (5 ÷ 5) + 2 = 9 + 1 + 2 = 12 ### Evaluate Numerical Expressions – UNLOCK the Problem – Page No. 50 Question 15. A movie theater has 4 groups of seats. The largest group of seats, in the middle, has 20 rows, with 20 seats in each row. There are 2 smaller groups of seats on the sides, each with 20 rows and 6 seats in each row. A group of seats in the back has 5 rows, with 30 seats in each row. How many seats are in the movie theater? a. What do you need to know? Type below: __________ Answer: We have to know the number of seats in each row to calculate the total number of seats. Question 15. b. What operation can you use to find the number of seats in the back group of seats? Write the expression. Type below: __________ Answer: A group of seats in the back has 5 rows with 30 seats in each row. So, to calculate the number of seats, we can use multiplication. Question 15. c. What operation can you use to find the number of seats in both groups of side seats? Write the expression. Type below: __________ Answer: 2 x (20 x 6) = 2 x 120 = 240 Question 15. d. What operation can you use to find the number of seats in the middle group? Write the expression. Type below: __________ Answer: 20 x 20 = (2 x 2) x (10 x 10) = 4 x 100 = 400 Question 15. e. Write an expression to represent the total number of seats in the theater. Type below: __________ Answer: (20 x 20) + (2 x 20 x 6) + (5 x 30) Question 15. f. How many seats are in the theater? Show the steps you use to solve the problem. _____ seats Answer: (20 x 20) + (2 x 20 x 6) + (5 x 30) = 400 + 240 + 150 = 640 + 150 = 790 Question 16. Test Prep In the wild, an adult giant panda eats about 30 pounds of food each day. Which expression shows how many pounds of food 6 pandas eat in 3 days? Options: a. 3 + (30 × 6) b. 3 × (30 × 6) c. (30 × 6) ÷ 3 d. (30 × 6) – 3 Answer: b. 3 × (30 × 6) Explanation: 1 panda eats 30 pounds of food each day. for 3 days, 3 x 30 = 90 1 panda eats 90 pounds of food in 3 days. 6 pandas can eat 90 x 6 = 540 pounds. 3 + (180) = 183 not equal to 540 pounds. 3 x (30 x 6) = 3 x (180) = 540 Question 17. Test Prep Which expression has a value of 6? Options: a. (6 ÷ 3) × 4 + 8 b. 27 – 9 ÷ 3 × ( 4 + 1) c. (18 + 12) × 6 – 4 d. 71 – 5 × (9 + 4) Answer: d. 71 – 5 × (9 + 4) Explanation: (6 ÷ 3) × 4 + 8 = 2 x 4 + 8 = 8 + 8 = 16 27 – 9 ÷ 3 × ( 4 + 1) = 27 – (9 ÷ 3) × 5 = 27 – 3 x 5 = 27 – 15 = 12 (18 + 12) × 6 – 4 = 180 – 4 = 176 71 – 5 × (9 + 4) = 71 – (5 x 13) = 71 – 65 = 6 ### Grouping Symbols – Share and Show – Page No. 53 Evaluate the numerical expression. Question 1. 12 + [(15 – 5) + (9 – 3)] 12 + [10 + ____] 12 +____ ____ Answer: 12 + [(15 – 5) + (9 – 3)] 12 + [10 + 6] 12 + 16 28 On Your Own Evaluate the numerical expression. Question 4. 4 + [(16 – 4) + (12 – 9)] ____ Answer: 4 + [(16 – 4) + (12 – 9)] 4 + [12 + 3] 4 + 15 = 19 Question 5. 24 – [(10 – 7) + (16 – 9)] ____ Answer: 24 – [(10 – 7) + (16 – 9)] 24 – [3 + 7] = 24 – 10 = 14 Question 6. 16 ÷ [(13 + 7) – (12 + 4)] ____ Answer: 16 ÷ [(13 + 7) – (12 + 4)] 16 ÷ [20 – 16] 16 ÷ 4 = 4 Question 7. 5 × [(7 – 2) + (10 – 8)] ____ Answer: 5 × [(7 – 2) + (10 – 8)] 5 x [5 + 2] 5 x 7 = 35 Question 8. [(17 + 8) + (29 – 12)] ÷ 6 ____ Answer: [(17 + 8) + (29 – 12)] ÷ 6 [25 + 17] ÷ 6 42 ÷ 6 = 7 Question 9. [(6 × 7) + (3 × 4)] – 28 ____ Answer: [(6 × 7) + (3 × 4)] – 28 [42 + 12] – 28 54 – 28 = 26 ### Grouping Symbols – UNLOCK the Problem – Page No. 54 Question 12. Dan has a flower shop. Each day he displays 24 roses. He gives away 10 and sells the rest. Each day he displays 36 carnations. He gives away 12 and sells the rest. What expression can you use to find out how many roses and carnations Dan sells in a week? a. What information are you given? Type below: __________ Answer: Each day, Dan displays 24 roses (gives away 10 and sells the rest), and he displays 36 carnations (gives away 12 and selles the rest). Question 12. b. What are you being asked to do? Type below: __________ Answer: We have to find out how many roses and carnations Dan sells in a week. Question 12. c. What expression shows how many roses Dan sells in one day? Type below: __________ Answer: 24 – 10 = 14 roses Question 12. d. What expression shows how many carnations Dan sells in one day? Type below: __________ Answer: 36 – 12 = 24 carnation Question 12. e. Write an expression to represent the total number of roses and carnations Dan sells in one day. Type below: __________ Answer: (24 – 10) + (36 – 12) = 14 + 24 = 38 roses and carnations Question 12. f. Write the expression that shows how many roses and carnations Dan sells in a week. Type below: __________ Answer: 7 x ((24 – 10) + (36 – 12)) = 7 x (14 + 24) = 7 x 38 = 266 roses and carnations Question 13. Evaluate the expression to find out how many roses and carnations Dan sells in a week. ____ flowers Answer: 7 x ((24 – 10) + (36 – 12)) 7 x (14 + 24) 7 x 38 = 266 roses and carnations Explanation: Question 14. Test Prep Which expression has a value of 4? Options: a. [(4 × 5) + (9 + 7)] + 9 b. [(4 × 5) + (9 + 7)] ÷ 9 c. [(4 × 5) – (9 + 7)] × 9 d. [(4 + 5) + (9 + 7)] – 9 Answer: b. [(4 × 5) + (9 + 7)] ÷ 9 Explanation: [(4 × 5) + (9 + 7)] + 9 = [20 + 16] + 9 = 36 + 9 = 45 [(4 × 5) + (9 + 7)] ÷ 9 = [20 + 16] ÷ 9 = 36 ÷ 9 = 4 ### Chapter Review/Test – Vocabulary – Page No. 55 Question 1. The ____ states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products. __________ Answer: Distributive Property Concepts and Skills Complete the sentence. Question 3. 50 is $$\frac{1}{10}$$ of _____ Answer: 500 Explanation: Let the unknown number is S. 50 = $$\frac{1}{10}$$ S S = 50 X 10 = 500 Complete the equation, and tell which property you used. Question 5. 45 + 16 =__ + 45 Type below: Type below: ________ Answer: 45 + 16 = 16 + 45; Commutative Property of Addition Explanation: 45 + 16 = 16 + 45; Commutative Property of Addition Find the value. Question 6. 102 = _____ Answer: 100 Explanation: 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; Estimate. Then find the product. Question 9. Estimate: 5 7 9 × 6 ———- Estimate: _____ Product: _____ Answer: Estimate: 3,600 Product: 3,474 Explanation: Estimate: 579 is close to 600; 600 x 6 = 3,600 579 x 6 6 x 9 =54; add ones and regroup tens 6 x 7 = 42; 42 + 5 = 47; add tens and regroup hundreds 6 x 5 = 30; 30 + 4 = 34 So, 3,474 is the product Question 10. Estimate: 7,316 × 6 ———- Estimate: _____ Product: _____ Answer: Estimate: 42,000 Product: 43,986 Explanation: Estimate: 7,316 is close to 7,000; 7,000 x 6 = 42,000 7,316 x 6 6 x 6 = 36; add ones and regroup tens 6 x 1 = 6; 6 + 3 = 18; add tens and regroup hundreds 6 x 3 = 18; 18 + 1 = 19; add hundreds and regroup thousads 6 x 7 = 42; 42 + 1 = 43 So, 43,986 is the product Question 11. Estimate: 4 3 6 × 3 2 ———- Estimate: _____ Product: _____ Answer: Estimate: 12,000 Product: 13,952 Explanation: Estimate: 436 is close to 400; 32 is close to 30 400 x 30 = 12,000 436 x 32; 436 x 2 = 872 436 x 30 = 13,080 13,080 + 872 = 13,952 Use multiplication and the Distributive Property to find the quotient. Evaluate the numerical expression. Question 15. 42 − (9 + 6) = _____ Answer: 42 − (9 + 6) 42 – 15 27 Question 16. 15 + (22 − 4) ÷ 6 = _____ Answer: 15 + (22 − 4) ÷ 6 15 + (18 ÷ 6) 15 + 3 18 Question 17. 6 × [(5 × 7) − (7 + 8)] = _____ Answer: 6 × [(5 × 7) − (7 + 8)] 6 x [35 – 15] 6 x [20] 120 ### Chapter Review/Test – Page No. 56 Fill in the bubble completely to show your answer. Question 18. Erica’s high score on her new video game is 30,000 points. Maria’s high score is $$\frac{1}{10}$$ of Erica’s. How many points did Maria score? Options: A. 30 B. 300 C. 3,000 D. 30,000 Answer: C. 3,000 Explanation: Erica’s high score on her new video game is 30,000 points. Maria’s high score is $$\frac{1}{10}$$ of Erica’s. 30,000 x $$\frac{1}{10}$$ = 3,000 Question 19. Rich makes$35 a week mowing lawns in his neighborhood. Which expression can be used to show how much money he makes in 8 weeks?
Options:
A. (8 × 30) + (8 × 5)
B. (8 × 30) + (8 × 5)
C. (8 + 30) × (8 + 5)
D. (8 × 30) × (8 × 5)

B. (8 × 30) + (8 × 5)

Explanation:
Rich makes $35 a week mowing lawns in his neighborhood. 8 x$35 = 8 x (30 + 5) = (8 x 30) + (8 x 5)

Question 20.
Mr. Rodriguez bought a supply of 20 reams of printer paper. Each ream contains 500 sheets of paper. How many sheets of printer paper are there?
Options:
A. 1,000
B. 5,000
C. 10,000
D. 100,000

C. 10,000

Explanation:
Mr. Rodriguez bought a supply of 20 reams of printer paper. Each ream contains 500 sheets of paper.
500 x 20 = 10,000

### Chapter Review/Test – Page No. 57

Question 22.
Megan used the following expression to find the quotient of a division problem.
(4 × 12) + (4 × 6)
What was the division problem and the quotient?
Options:
A. 24 ÷ 4 = 6
B. 48 ÷ 4 = 12
C. 64 ÷ 4 = 16
D. 72 ÷ 4 = 18

D. 72 ÷ 4 = 18

Explanation:
Megan used (4 × 12) + (4 × 6)
4 x (12 + 6)
4 x 18 = 72
72 ÷ 4 = 18

Question 23.
It is 1,325 feet from Kinsey’s house to her school. Kinsey walks to school each morning and gets a ride home each afternoon. How many feet does Kinsey walk to school in 5 days?
Options:
A. 6,725 feet
B. 6,625 feet
C. 6,525 feet
D. 5,625 feet

B. 6,625 feet

Explanation:
It is 1,325 feet from Kinsey’s house to her school. Kinsey walks to school each morning and gets a ride home each afternoon.
1,325 feet x 5 = 6,625 feet

Question 24.
An adult elephant eats about 300 pounds of food each day. Which expression shows about how many pounds of food a herd of 12 elephants eats in 5 days?
Options:
A. 5 + (300 × 12)
B. 5 × (300 × 12)
C. (300 × 12) ÷ 5
D. (300 × 12) − 5

B. 5 × (300 × 12)

Explanation:
(300 x 12)
In 5 days, 5 × (300 × 12)

Question 25.
Carla can type 265 characters a minute on her computer keyboard. At that rate, how many characters can she type in 15 minutes?
Options:
A. 2,975
B. 3,875
C. 3,905
D. 3,975

D. 3,975

Explanation:
Carla can type 265 characters a minute on her computer keyboard.
In 15 minutes, 265 x 15 = 3,975

### Chapter Review/Test – Page No. 58

Constructed Response

Question 26.
Donavan copied the problem below from the board. He missed one of the numbers needed to show his work. What number is missing in his work? Explain how you found the missing number

17 × 5 = ( ______ +7) × 5
= ( ______ × 5) + (7 × 5)

Missing number is 10. Using the Distributive Property, the sum of the two number within the () has to be equal to the other factor 17.
10 + 7 = 17
17 × 5 = ( 10 +7) × 5
= ( 10 × 5) + (7 × 5)

Question 27.
Drew’s weekly allowance is $8.00. His friend Jan’s weekly allowance is$10. Drew spends $3 a week and Jan spends$4 a week.
A. Write two expressions to show how much money each person has at the end of the week. Use parentheses.
Drew has __ .
Jan has __ .
Type below:
__________

Drew has ($8 –$3) .
Jan has ($10 –$4).

Question 27.
B. Drew and Jan decide that they want to put their money together to buy a video game. Write an expression that shows how much they can save each week. Explain.
Type below:
__________

(8 – 3) + (10 – 4); Add the amount of money Drew and Jan have at the end of the week. This equals the amount they can save a week.

Question 27.
C. The video game Drew and Jan want to buy costs \$55. Write an expression to show how many weeks it will take them to save enough to buy the video game. Use parentheses and brackets in your expression. Then evaluate the expression.
_____ weeks