All the solutions provided in **McGraw Hill My Math Grade 3 Answer Key PDF Chapter 13 Lesson 7 Area and the Distributive Property **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 3 Answer Key Chapter 13 Lesson 7 Area and the Distributive Property

**Draw It**

The grid shows a rectangle with a length of 6 units and a width of 5 units. If the length of this rectangle increased by 2 units, what would be the new area?

The area of the rectangle is ____________ square units.

Label this rectangle A.

1. Shade more unit squares so that the length of the rectangle is now increased by 2 units, but the width remains unchanged.

2. Label the additional rectangle formed by w what you shaded as Rectangle B. What is the area of Rectangle B?

3. Add the areas of rectangles A and B.

The area of the larger rectangle is ______________ square units.

Check: The length of the larger rectangle is 8 units. The width is 5 units. 8 × 5 = 40

Answer:

The area of the rectangle is 30 square units.

Area of rectangle A and B

A = (6 × 5) + (2 × 5)

A = 30 + 10

A = 40

The area of the larger rectangle is 40 square units.

**Try It**

Use the Distributive Property to find the area of the rectangle.

1. Decompose one factor.

12 = 10 + 2

2. Find the area of each smaller rectangle. Then add.

So, the area of the rectangle is ___________ square units.

Answer:

7 × 12 = (7 × 10) + (7 × 2)

= 70 + 14

= 84

So, the area of the rectangle is 84 square units.

**Talk About It**

Question 1.

**Mathematical PRACTICE** Justify Conclusions Refer to the second activity. If you decomposed 12 into 9 + 3 instead of 10 + 2, how would that have affected the result?

Answer:

No, it would not have affected the answer.

Question 2.

How can the Distributive Property help you find the area of rectangles with greater numbers?

Answer: It can break up the numbers and help you multiply and add numbers together easily.

**Practice It**

**Use the Distributive Property to find the area of each rectangle.**

Question 3.

The area is _____________ square units.

Answer:

6 × 7 = (6 × 5) + (6 × 2)

= 30 + 12

= 42

The area is 42 square units.

Question 4.

The area is _____________ square units.

Answer:

8 × 9 = (8 × 5) + (8 × 4)

= 40 + 32

= 72

The area is 72 square units.

**Find the area of each rectangle. Use the Distributive Property to decompose the longer side into a sum. Show your steps.**

Question 5.

The area is _______________ square centimeters.

Answer:

l = 11 cm

w = 4 cm

Area = 11 × 4

= 44 sq. cm

The area is 44 square centimeters.

Question 6.

The area is _______________ square feet.

Answer:

l = 5 ft

w = 12 ft

Area = 5 × 12

= 60 sq.ft

The area is 60 square feet.

**Apply It**

Question 7.

Julia is planting vegetables in her rectangular garden. Her garden has a length of 8 feet and a width of 12 feet. Use the Distributive Property to decompose the factor 12 into a sum. Then find the area of the garden.

Answer:

Given,

Julia is planting vegetables in her rectangular garden. Her garden has a length of 8 feet and a width of 12 feet.

A = 8 × 12

A = (8 × 10) + (8 × 2)

= 80 + 16

= 96 sq. ft

Question 8.

Matthew is carpeting the rectangular floor in his bedroom. The floor has a length of 15 feet and a width of 9 feet. Use the Distributive Property to decompose the factor 15 into a sum. Then find the area of the floor.

Answer:

Given,

Matthew is carpeting the rectangular floor in his bedroom. The floor has a length of 15 feet and a width of 9 feet.

A = 15 × 9

A = (9 × 10) + (9 × 5)

A = 90 + 45

A = 135 sq. ft

Question 9.

**Mathematical PRACTICE** Reason Describe three ways to find the area of a rectangle with a length of 9 meters and a width of 4 meters.

Answer:

1. A = 9 × 4 = 36 sq .m

2. A = 4 × 9 = 36 sq .m

3. A = (9 × 2) + (9 × 2) = 18 + 18 = 36 sq .m

Question 10.

**Mathematical PRACTICE** Find the Error James needed to find the area of a rectangle with a length of 11 inches and a width of 9 inches. His steps are to the right. Find and correct his error.

9 × 11 = (9 × 10) + (9 × 2)

= 90 + 18

= 108

Answer:

The mistake happened at 9 × 2, it should have been (9 × 1) + (9 × 10) = 9 + 90 = 99

**Write About It**

Question 11.

How are the operations of addition and multiplication used when finding area using the Distributive Property?

Answer:

When you break up the numbers you are adding, multiplying the 2 numbers and add the products.

### McGraw Hill My Math Grade 3 Chapter 13 Lesson 7 My Homework Answer Key

**Practice**

Question 1.

Use the Distributive Property to find the area of the rectangle.

Answer:

6 × 9 = (6 × 5) + (6 × 4)

= 30 + 24

= 54 sq. units

Question 2.

Use the Distributive Property to find the area of the rectangle.

Answer:

8 × 12 = (8 × 10) + (8 × 2)

= 80 + 16 = 96 sq. units

**Find the area of each rectangle. Use the Distributive Property to decompose the longer side. Show your steps.**

Question 3.

The area is _____________ square inches.

Answer:

s = 9 in.

Area = 9 × 9 = 81

The area is 81 square inches.

Question 4.

The area is _____________ square meters.

Answer:

l = 8 m

w = 11 m

Area = 8 × 11 = 88

The area is 88 square meters.

**Problem Solving**

Question 5.

**Mathematical PRACTICE** Identify Structure Erika is painting a- rectangular painting. The painting has a length of 12 inches and a width of 10 inches. Use the Distributive Property to decompose the factor 12. Then find the area of the painting.

Answer:

Given,

The painting has a length of 12 inches and a width of 10

A = 12 × 10 = 120

Thus the area of the painting is 120 sq. inches

Question 6.

Hector will build a deck in his backyard. The deck ‘has a length of 9 meters and a width of 8 meters. Use the Distributive Property to decompose the factor 9. Then find the area of the deck.

Answer:

Given,

The deck ‘has a length of 9 meters and a width of 8 meters

A = 9 × 8

= 72 sq. meters

Distributive Property

A = (9 × 4) + (9 × 4)

A = 36 + 36

A = 72 sq. meters

Thus the area of the deck is 72 sq. meters