All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 2 Lesson 6 Use Partial Products and the Distributive Property** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 2 Lesson 6 Use Partial Products and the Distributive Property

**Draw It**

Darnel and his four friends went to an ice skating rink and bought sandwiches. They divided the total cost and found that each person needs to pay $17. What was the total cost for ice skating and sandwiches?

Find 5 × 17 using an area model.

1. Label the model to find the partial products.

Answer:

2. Add the partial products.

___ + ___ = ____

So, the total cost for ice skating and sandwiches was _____.

Answer:

The partial products are 50 + 35 = 85

So, the total cost for ice skating and sandwiches was 85.

When you use partial products, you are using a property. A property is a rule in mathematics that can be applied to all numbers. The property that you applied above is called the Distributive Property. You will learn more about this property in the next lesson.

**Try It**

**Find 7 × 56 using an area model.**

1. Label the model to find partial products.

Answer:

2. Multiply. Then add.

7 × 56 = (7 × 50) + (7 × ___)

= ____ + ____

= _____

So, 7 × 56 = ____

Answer:

392

Explanation:

7 × 56 = (7 × 50) + (7 × 6)

= 350 + 42

= 392

So, 7 × 56 = ____

392

**Talk About It**

Question 1.

**Mathematical PRACTICE 3** Draw a Conclusion How do area models show partial products?

Answer:

Question 2.

In finding 7 × 56 above, why does the area model separate 56 into 50 and 6?

Answer:

The area model separates 56 into 50 and 6 to calculate the multiplication easily.

Question 3.

Find 6 × 36 using partial products. Label the model to help you solve. Show your work.

Answer:

**Practice It**

**Multiply using the area model. Label each model.**

Question 4.

4 × 16 = ____

Answer:

64

Explanation:

Question 5.

6 × 81 = ____

Answer:

486

Explanation:

Question 6.

7 × 29 = ___

Answer:

203

Explanation:

Question 7.

5 × 39 = ___

Answer:

195

Explanation:

**Apply It**

Question 8.

Ronnie swims 4 laps each day at the pool. How many laps does he swim in 28 days? Use an area model to solve.

Answer:

4 × 28 = 112

Explanation:

4 × 20 + 4 × 8

80 + 32

112

Question 9.

**Mathematical PRACTICE Model Math** Yoshi saved $5 each week for 23 weeks. What is the total amount of money he saved? Use an area model to solve.

Answer:

5 × 23 = 115

Explanation:

5 × 20 + 5 × 3

100 + 15

115

Question 10.

Thirty-eight fish are in each aquarium at a fish store. How many fish are there in five aquariums? Use an area model to solve.

Answer:

38 × 5 = 190

Explanation:

Question 11.

**Mathematical PRACTICE** **Find the Error** Omar was using an area model to find 4 × 61. Find his mistake and correct it.

(4 × 60) + (4 × 10) = 240 + 40 = 280

Answer:

The answer is 244, not 280.

Explanation:

(4 × 60) + (4 × 1)

240 + 4

244

**Write About It**

Question 12.

How can area models be used to solve multiplication problems?

Answer:

### McGraw Hill My Math Grade 5 Chapter 2 Lesson 6 My Homework Answer Key

**Practice**

Question 1.

Multiply 2 × 27 using the area model. Label the model.

2 × 27 = _____

Answer:

54

Explanation:

2 × 20 + 2 × 7

40 + 14

54

Question 2.

Multiply 9 × 43 using the area model. Label the model.

9 × 43 = _____

Answer:

387

Explanation:

9 × 40 + 9 × 3

360 + 27

387

**Problem Solving**

Question 3.

A pet store has eighteen hamsters in each cage. How many hamsters are there in six cages? Usé an area model to solve.

Answer:

18 × 6 = 108

Explanation:

6 × 10 + 6 × 8

60 + 48

108

Question 4.

**Mathematical PRACTICE 4 Model Math** Brandon packs his lunch 4 days each week. How many days does he pack his lunch for 36 weeks? Use an area model to solve.

Answer:

Bradon packs 144 days in 36 weeks.

Explanation:

We need to find the number of days he packs his lunch for 36 weeks.

4 × 36 = 144

The area model is shown in figure

4 × 36 = (4 × 30) + (4 + 6)

= 120 + 24

= 144

Question 5.

Ricarda earns a $25 allowance each week. How much allowance will she earn after 7 weeks? Use an area model to solve.

Answer:

$175

Explanation:

Ricarda earns a $25 allowance each week.

5 × 7 = 35

20 × 7 = 140

140 + 35 = 175

The allowance will she earn after 7 weeks is $175.

Question 6.

Write an expression that uses partial products to multiply 8 × 64.

Answer:

(80 × 6) + (8 × 4)