All the solutions provided in **McGraw Hill My Math Grade 3 Answer Key PDF Chapter 9 Lesson 2 Two Distributive Property **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 3 Answer Key Chapter 9 Lesson 2 Two Distributive Property

The Distributive Property allows you to decompose one factor. Then you can use smaller known facts to find products.

**Math in My World**

**Example 1**

Henry’s Hardware Store sells wrench sets. Each set holds 6 wrenches. How many wrenches are there in 8 sets?

Find 8 × 6.

Decompose one factor.

One way is to decompose 6 into 5 + 1.

So, 8 × 6 = ____________. There are ___________ wrenches.

Answer: 8 × 6 = 48 , There are 48 wrenches

Explanation:

Given, 8 × 6

decompose the factor 6 into 5 + 1.

8 × 6 = ( 8 × 5 ) + ( 8 × 1 )

48 = 40 + 8

48 = 48

8 × 6 = 48

So, There are 48 wrenches

**Example 2**

Karma’s dad used 7 boards to build a picnic table. How many nails were used if each board needed 7 nails?

Find 7 × 7.

Decompose one factor.

One way is to decompose 7 into 5 + 2.

So, Karma and her dad used _____________ nails altogether.

Answer: Karma and her dad used 49 nails altogether.

Explanation:

Given, 7 × 7

decompose the factor 7 into 5 + 2.

7 × 7 = ( 7 × 5 ) + ( 7 × 2 )

49 = 35 + 14

49 = 49

7 × 7 = 49

So, Karma and her dad used 49 nails altogether.

**Talk Math**

Explain what it means to decompose a number.

Answer: To decompose in math is to break down numbers into parts. Add: To add is to join two numbers together. Subtract: To subtract is to take away from another to see the difference. Place Value: Place value is the value represented by a digit in a number on the basis of its position in the number.

**Guided Practice**

**Use the Distributive Property to find each product.**

Question 1.

Answer:

Explanation:

Given, 8 × 3

By using Distributive Property we get.

8 × 3 = ( 8 × 2 ) + ( 8 × 1 )

= 16 + 8

= 24

So, 8 × 3 = 24.

Question 2.

Answer:

Explanation:

Given, 8 × 8

By using Distributive Property we get.

8 × 8 = ( 8 × 4 ) + ( 8 × 4 )

= 32 + 32

= 64

So, 8 × 8 = 64.

**Independent Practice**

**Use the Distributive Property to find each product.**

Question 3.

4 × 6 = ____________

Answer: 4 × 6 = 24

Explanation:

Given, 4 × 6

By using Distributive Property we get.

4 × 6 = ( 4 × 3 ) + ( 4 × 3 )

= 12 + 12

= 24

So, 4 × 6 = 24.

Question 4.

6 × 6 = ______________

Answer: 6 × 6 = 36

Explanation:

Given, 6 × 6

By using Distributive Property we get.

6 × 6 = ( 6 × 3 ) + ( 6 × 3 )

= 18 + 18

= 36

So, 6 × 6 = 36.

Question 5.

8 × 9 = _____________

Answer: 8 × 9 = 72

Explanation:

Given, 8 × 9

By using Distributive Property we get.

8 × 9 = ( 8 × 5 ) + ( 8 × 4 )

= 40 + 32

= 72

So, 8 × 9 = 72.

Question 6.

10 × 4 = ______________

Answer: 10 × 4 = 40

Explanation:

Given, 10 × 4

By using Distributive Property we get.

10 × 4 = ( 4 × 5 ) + ( 4 × 5 )

= 20 + 20

= 40

So, 10 × 4 = 40.

Question 7.

12 × 4 = _______________

Answer: 12 × 4 = 48

Explanation:

Given, 12 × 4

By using Distributive Property we get.

12 × 4 = ( 6 × 4 ) + ( 6 × 4 )

= 24 + 24

= 48

So, 12 × 4 = 48.

Question 8.

11 × 8 = ________________

Answer: 11 × 8 = 88

Explanation:

Given, 11 × 8

By using Distributive Property we get.

11 × 8 = ( 11 × 4 ) + ( 11 × 4 )

= 44 + 44

= 88

So, 11 × 8 = 88.

Question 9.

10 × 10 = _______________

Answer: 10 × 10 = 100

Explanation:

Given, 10 × 10

By using Distributive Property we get.

10 × 10 = ( 10 × 5 ) + ( 10 × 5 )

= 50 + 50

= 100

So, 10 × 10 = 100.

Question 10.

12 × 6 = ________________

Answer: 12 × 6 = 72

Explanation:

Given, 8 × 8

By using Distributive Property we get.

12 × 6 = ( 12 × 3 ) + ( 12 × 3 )

= 36 + 36

= 72

So, 12 × 6 = 72.

**Problem Solving**

Question 11.

**Mathematical PRACTICE** Identify Structure The Fix It Right Hardware Store is open 12 hours every day. How many hours are they open altogether from Monday through Friday?

Answer: They are open 60 hours altogether from Monday through Friday.

Explanation:

Given, The Fix It Right Hardware Store is open 12 hours every day.

How many hours are they open altogether from Monday through Friday

12 hours for 5 days

Then, 12 × 5

decompose the factor 6 into 5 + 1.

12 × 5 = ( 6 × 5 ) + ( 6 × 5 )

= 30 + 30

= 60

12 × 5 = 60

So, They are open 60 hours altogether from Monday through Friday.

Question 12.

A restaurant orders 9 dozen eggs. The picture shows the number of eggs from each dozen that broke during shipping. How many eggs are unbroken? (Hint: 1 dozen = 12)

Answer: 103 eggs are unbroken

Explanation:

Given, A restaurant orders 9 dozen eggs.

1 dozen = 12

Then, 12 × 9 = ( 6 × 9 ) + ( 6 × 9 )

= 54 + 54

= 108

12 × 9 = 108

totally 108 eggs are there

Among them 5 eggs are broken

108 – 5 = 103

So, 103 eggs are unbroken

Question 13.

Each aquarium has 10 clown fish and 6 puffer fish. There are 7 aquariums. How many fish are there in all?

Answer: There are 112 fish in all the aquarium

Explanation:

Given, Each aquarium has 10 clown fish and 6 puffer fish.

That means, 10 + 6 = 16 fish in an Aquarium

There are 7 Aquariums

16 × 7 = ( 7 × 10 ) + ( 7 + 6 )

= 70 + 42

= 112

So, There are 112 fish in all the aquarium.

**HOT Problems**

Question 14.

**Mathematical PRACTICE** Make Sense of Problems There are 12 inches in one foot and 3 feet in one yard. How many inches are in 2 yards?

Answer: There are 72 inches in 2 yards

Explanation:

Given, There are 12 inches in one foot and 3 feet in one yard.

That means, 12 × 3 = 36

Then for 2 yards ,it will be

36 + 36 = 72

So, There are 72 inches in 2 yards.

Question 15.

**Building on the Essential Question** How are parentheses used when grouping factors?

Answer: Parentheses are for the innermost group. If a second grouping , which will include the part already in parentheses, is needed, square brackets are used. If a third grouping, which will include a section with parentheses and square brackets, is necessary, then braces are used.

### McGraw Hill My Math Grade 3 Chapter 9 Lesson 2 My Homework Answer Key

**Practice**

**Use the Distributive Property to find each product.**

Question 1.

4 × 9 = ______________

Answer: 4 × 9 = 36

Given, 4 × 9

By using Distributive Property we get.

4 × 9 = ( 4 × 5 ) + ( 4 × 4 )

= 20 + 16

= 36

So, 4 × 9 = 36.

Question 2.

5 × 6 = ______________

Answer: 5 × 6 = 30

Given, 5 × 6

By using Distributive Property we get.

5 × 6 = ( 5 × 3 ) + ( 5 × 3 )

= 15 + 15

= 30

So, 5 × 6 = 30.

Question 3.

5 × 11 = _______________

Answer: 5 × 11 = 55

Given, 5 × 11

By using Distributive Property we get.

5 × 11 = ( 5 × 6 ) + ( 5 × 5 )

= 30 + 25

= 55

So, 5 × 11 = 55.

Question 4.

12 × 7 = ______________

Answer: 12 × 7 = 84

Given, 12 × 7

By using Distributive Property we get.

12 × 7 = ( 6 × 7 ) + ( 6 × 7 )

= 42 + 42

= 84

So, 12 × 7 = 84.

**Problem Solving**

Question 5.

Milly bought 4 bags of apples at the grocery store. Each bag contains 6 apples. How many apples does Milly have in all?

Answer: Milly has 24 apples in all

Explanation:

Given, Milly bought 4 bags of apples at the grocery store.

Each bag contains 6 apples.

6 × 4 = 24

So, Milly has 24 apples in all

Question 6.

**Mathematical PRACTICE** Identify Structure Byron scrambled 8 dozen eggs for the campers. What is the total number of eggs Byron scrambled? (Hint: 1 dozen = 12)

Answer: Byron has scrambled 96 eggs

Explanation:

Given, Byron scrambled 8 dozen eggs for the campers.

1 dozen = 12 eggs

Then, 8 dozen eggs are ,

12 × 8 = 96

So, Byron has scrambled 96 eggs.

Question 7.

There are 6 seats in each row in the theater. If 8 rows are filled with people, how many people are in the theater?

Answer: 48 people are there in the theater

Explanation:

Given, There are 6 seats in each row in the theater,

If 8 rows are filled with people,

6 × 8 = 48

So, 48 people are there in the theater.

**Vocabulary Check**

Question 8.

Explain how you could use the Distributive Property to decompose a factor and find the product of 5 × 9.

Answer: 5 × 9 = 45

Explanation:

Given, 5 × 9

By using Distributive Property to decompose a factor 9 in to 6 + 3 ,

we get.

5 × 9 = ( 5 × 6 ) + ( 5 × 3 )

= 30 + 15

= 45

So, 5 × 9 = 45.

**Test Practice**

Question 9.

Which shows the correct use of the Distributive Property to find 4×12?

(A) (2 × 6) + (2 × 6)

(B) (4 × 10) + (4 × 2)

(C) (4 × 6) + (2 × 6)

(D) (4 × 8) + (4 × 3)

Answer: B

Explanation:

Given, 4 × 12

By using Distributive Property we get.

4 × 12 = ( 4 × 10 ) + ( 4 × 2 )

= 40 + 8

= 48

4 × 12 = 48.

So, (4 × 10) + (4 × 2) is the correct option.