All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 2 Lesson 7 The Distributive Property** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 2 Lesson 7 The Distributive Property

Example 1

For a field trip, 42 students each paid $3 for transportation Use mental math and the Distributive Property to find how much money was collected altogether.

Find 3 × 42.

So, $_____ was collected for the field trip.

Answer:

126

Explanation:

Example 2

Find 7 × 26 mentally using the Distributive Property. Show the steps that you used.

So, 7 × 26 = ___

Answer:

182

Explanation:

**Guided Practice**

**Find each product mentally using the Distributive Property. Show the steps that you used.**

Question 1.

5 × 18

5 × 18 = 5 × (___ + 8)

= (5 × ___) + (5 × ___)

= ____ + ____

= _____

So, 5 × 18 = ____

Answer:

90

Explanation:

5 × 18

5 × 18 = 5 × (10 + 8)

= (5 × 10) + (5 × 8)

= 50 + 40

= 90

So, 5 × 18 = 90

Question 2.

2 × 21

2 × 21 = 2 × (___ + ___)

= (2 × ___) + (2 × ___)

= ____ + ____

= _____

So, 2 × 21 = ____

Answer:

42

Explanation:

2 × 21

2 × 21 = 2 × (20 + 1)

= (2 × 20) + (2 × 1)

= 40 + 2

= 42

So, 2 × 21 = 42

**Independent Practice**

**Find each product mentally using the Distributive Property. Show the steps that you used.**

Question 3.

6 × 13 = ___

Answer:

78

Explanation:

Given multiplicand is 6 and the multiplier is 13.

By multiplying both multiplicand 6 and multiplier 13, we get the value 78

The multiplication of the given number 6 × 13 = 78

Question 4.

3 × 52 = ____

Answer:

156

Explanation:

Given multiplicand is 3 and the multiplier is 52.

By multiplying both multiplicand 3 and multiplier 52, we get the value 156.

The multiplication of the given number 3 × 52 = 156

Question 5.

5 × 26 = ___

Answer:

130

Explanation:

Given multiplicand is 5 and the multiplier is 26.

By multiplying both multiplicand 5 and multiplier 26, we get the value 130.

The multiplication of the given number 5 × 26 = 130

Question 6.

4 × 69 = ___

Answer:

276

Explanation:

Given multiplicand is 4 and the multiplier is 69.

By multiplying both multiplicand 4 and multiplier 69, we get the value 276.

The multiplication of the given number 4 × 69 = 276

Question 7.

2 × 49 = ___

Answer:

98

Explanation:

Given multiplicand is 2 and the multiplier is 49.

By multiplying both multiplicand 2 and multiplier 49, we get the value 98.

The multiplication of the given number 2 × 49 = 98

Question 8.

7 × 23 = ___

Answer:

161

Explanation:

Given multiplicand is 7 and the multiplier is 23.

By multiplying both multiplicand 7 and multiplier 23, we get the value as 161.

The multiplication of the given number 7 × 23 = 161

Question 9.

26 × 6 = ___

Answer:

156

Explanation:

Given multiplicand is 26 and the multiplier is 6.

By multiplying both multiplicand 26 and multiplier 6, we get the value as 156.

The multiplication of the given number 26 × 6 = 156.

Question 10.

55 × 4 = ___

Answer:

220

Explanation:

Given multiplicand is 55 and the multiplier is 4.

By multiplying both multiplicand 55 and multiplier 4, we get the value as 220.

The multiplication of the given number 55 × 4 = 220.

**Problem Solving**

Question 11.

A horse is 17 hands tall. If a hand equals 4 inches, how tall is the horse in inches? Use the Distributive Property to solve.

Answer:

68 inches.

Explanation:

A horse is 17 hands tall. If a hand equals 4 inches

17 × 4 = 68 inches.

Question 12.

Mr. Collins is buying 5 train tickets for $36 each. What is the total cost of the tickets? Use the Distributive Property to solve.

Answer:

$180

Explanation:

From the given question find 36 × 5 = 180

The total cost of the ticket is $180

Question 13.

Melanie runs 23 miles each week. How many miles does she run in 9 weeks? Use the Distributive Property to solve.

Answer:

207 miles

Explanation:

23 × 9

The distributive property is as follows

(20 + 3) × 9

20 × 9 + 3 × 9

180 + 27

207 miles

**Hot Problems**

Question 14.

**Mathematical PRACTICE** **Find the Error** Dylan is using the Distributive Property to simplify 6 × (9 + 4). Find his mistake and correct it.

6 × (9 + 4) = 54 + 4

= 58

Answer:

6 × (9 + 4) = 6 × 13

= 78

Explanation:

Dylan didn’t follow the arithmetic rule. He doesn’t do the parentheses first.

6 × (9 + 4) = 6 × 13

= 78

Question 15.

**? Building on the Essential Question** How can the Distributive Property be used to multiply numbers? Explain.

Answer: You can use the distributive property to multiply numbers by changing the order of the numbers you’re multiplying and still achieve the same correct answer.

### McGraw Hill My Math Grade 5 Chapter 2 Lesson 7 My Homework Answer Key

**Practice**

**Find each product mentally using the Distributive Property. Show the steps that you used.**

Question 1.

4 × 48 = ___

Answer:

192

Explanation:

Given multiplicand is 4 and the multiplier is 48.

By multiplying both multiplicand 4 and multiplier 48, we get the value as 192.

The multiplication of the given number 4 × 48 is 192.

Question 2.

3 × 67 = ____

Answer:

201

Explanation:

Given multiplicand is 3 and the multiplier is 67.

By multiplying both multiplicand 3 and multiplier 67, we get the value as 201.

The multiplication of the given number 3 × 67 is 201.

Question 3.

6 × 18 = ____

Answer:

108

Explanation:

Given multiplicand is 6 and the multiplier is 108.

By multiplying both multiplicand 6 and multiplier 108, we get the value as 108.

The multiplication of the given number 6 × 18 = 108.

Question 4.

8 × 74 = ___

Answer:

592

Explanation:

Given multiplicand is 8 and the multiplier is 74.

By multiplying both multiplicand 8 and multiplier 74, we get the value as 592.

The multiplication of the given number 8 × 74 = 592.

**Problem Solving**

Question 5.

A bookshelf in Deirdre’s living room has 4 shelves. There are 12 books on each shelf. How many books are on the bookshelf altogether?

Answer:

48

Explanation:

From the given question find 4 × 12

48

Hence there are 48 books are on the bookshelf altogether.

Question 6.

Jorge is collecting baseball cards. He has 29 stacks of cards with 4 in each stack. How many cards does he have altogether?

Answer:

116

Explanation:

From the given question find = 29 × 4

= 116

Question 7.

**Mathematical PRACTICE 3** **Justify Conclusions** The Distributive Property also combines subtraction and multiplication. For example, 3 × (5 – 2) = (3 × 5) – (3 × 2). Explain how you could use the Distributive Property and mental math to find 5 × 198.

Answer:

The value of 5 × 198 is 990.

Explanation:

The distributive property is a(b + c) = ab + ac

The given expression is 5 × 198.

5 × (100 + 90 + 8)

5 × 100 + 5 × 90 + 5 × 8

500 + 450 + 40

990.

**Vocabulary Check**

**Fill in each blank with the correct term or number to complete the sentence.**

Question 8.

The Distributive Property combines ____ and ____ to make multiplying whole numbers simpler.

Answer:

Addition and multiplication

Explanation:

The Distributive Property combines addition and multiplication to make multiplying whole numbers simpler.

**Test Practice**

Question 9.

Susana collected 5 cents at the recycling plant for each of her 78 cans. How much money did she collect altogether?

A. $0.39

B. $3.50

C. $3.90

D. $39.00

Answer:

$3.90

Explanation:

Susana collected 5 cents at the recycling plant for each of her 78 cans

5 × 78 = 390

1 dollar = 100 cents

390 ÷ 100 = $3.90