All the solutions provided in **McGraw Hill Math Grade 4 Answer Key PDF Chapter 3 Lesson 6 The Associative Property of Multiplication** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 3 Lesson 6 The Associative Property of Multiplication

**Math in My World**

Example 1

There are 2 video games in each value pack. There are 6 value packs in each box. If Raul buys 3 boxes for his collection, how many video games will he have?

You need to find 2 × 6 × 3. There are two ways to group the numbers.

**One Way**

Multiply 2 × 6 first.

**Helpful Hint**

Use repeated addition to find 12 × 3. ____

12 + 12 + 12 =

=

**Another Way**

Multiply 6 × 3 first.

**Helpful Hint**

Use repeated addition to find 18 × 2.

18 + 18 =

=

So, Raul will have ____ video games.

Answer:

There are 2 video games in each value pack.

There are 6 value packs in each box.

Raul buys 3 boxes.

Using the Associative Property of Multiplication

First multiply 2 x 6.

Using the repeated addition 12 × 3 is

12 + 12 + 12 = 36.

The another way is 6 x 3 first.

Using the repeated addition 18 × 2 is

18 + 18 = 36.

So, Raul will have 36 video games.

**Helpful Hint**

Example 2

Use the Associative Property of Multiplication to find 9 × 2 × 4.

**Helpful Hint**

Parentheses () tell you which numbers to multiply first

Answer:

**Talk Math**

Identify the order that makes it easier to multiply the factors in 9 × 4 × 2. Explain.

Answer:

To multiply the factors 9 x 4 x 2 you can use associative property of multiplication.

In this first multiply 9 x 4 or 4 x 2.

9 x 4 = 36

36 x 2 = 72.

or

4 x 2 = 8.

9 x 8 = 72.

**Guided Practice**

**Multiply. Use the Associative Property.**

Question 1.

Answer:

Using the Associative property of multiplication

First multiply 3 x 3.

3 x 3 = 9.

Then 5 x 9 = 45.

Therefore the product is 45.

Question 2.

Answer:

Using the Associative property of multiplication

First multiply 4 x 2.

Multiplication of 4 with 2 then you get 8.

4 x 2 = 8.

Then 8 x 7 = 56.

Therefore the product is 56.

Question 3.

Answer:

Using the Associative property of multiplication

First multiply 3 x 1.

Multiplication of 3 with 1 then you get 3.

3 x 1 = 3.

Then 3 x 6 = 18.

Therefore the product is 18.

**Independent Practice**

**Multiply. Use the Associative Property.**

Question 4.

6 × 1 × 5 = ____

Answer:

Using the associative property.

(6 x 1) x 5 = 6 x (1 x 5)

6 x 5 = 6 x 5

30 = 30.

Therefore the product is 30.

Question 5.

2 × 2 × 7 = ____

Answer:

Using the associative property.

(2 x 2) x 7 = 2 x (2 x 7)

4 x 7 = 2 x 14.

28 = 28.

Therefore the product is 28.

Question 6.

7 × 5 × 2 = ___

Answer:

Using the associative property.

(7 x 5) x 2 = 7 x (5 x 2)

35 x 2 = 7 x 10.

70 = 70.

Therefore the product is 70.

Question 7.

10 × 2 × 5 = ____

Answer:

Using the associative property.

(10 x 2) x 5 = 10 x (2 x 5)

20 x 5 = 10 x 10.

100 = 100.

Therefore the product is 100.

Question 8.

9 × 3 × 3 = ____

Answer:

Using the associative property.

(9 x 3) x 3 = 9 x (3 x 3)

27 x 3 = 9 x 9.

81 = 81

Therefore the product is 81.

Question 9.

6 × 2 × 2 = ___

Answer:

Using the associative property.

(6 x 2) x 2 = 6 x (2 x 2)

12 x 2 = 6 x 4.

24 = 24.

Therefore the product is 24.

Question 10.

2 × 3 × 7 = ____

Answer:

Using the associative property.

(2 x 3) x 7 = 2 x (3 x 7)

6 x 7 = 2 x 21

42 = 42.

Therefore the product is 42.

Question 11.

9 × 2 × 4 = ____

Answer:

Using the associative property.

(9 x 2) x 4 = 9 x (2 x 4)

18 x 4 = 9 x 8.

72 = 72.

Therefore the product is 72.

Question 12.

5 × 1 × 10 = ____

Answer:

Using the associative property.

5 x (1 x 10) = (5 x 1) x 10.

5 x 10 = 5 x 10.

50 = 50.

Therefore the product is 50.

**Compare. Use >, <, or =.**

Question 13.

4 × 2 × 9 7 × 4 × 2

Answer:

Using the associative property.

4 x (2 x 9) = (4 x 2) x 9.

4 x 18 = 8 x 9

72 = 72.

The product is 72.

And

(7 x 4) x 2 = 7 x (4 x 2)

28 x 2 = 7 x 8.

56 = 56.

The product is 56.

4 × 2 × 9 > 7 × 4 × 2.

Question 14.

6 × 2 × 6 5 × 2 × 8

Answer:

Using the associative property.

6 x (2 x 6) = (6 x 2) x 6.

6 x 12 = 12 x 6

72 = 72.

The product is 72.

And

(5 x 2) x 8 = 5 x (2 x 8)

10 x 8 = 5 x 16.

80 = 80.

The product is 80.

6 × 2 × 6 < 5 × 2 × 8

**Find the value of each number sentence if = 2, = 3, and = 4.**

Question 15.

5 × 1 × = ____

Answer:

Given object = 4.

5 x 1 x 4.

Using the associative property of multiplication.

(5 x 1) x 4 = 5 x (1 x 4)

5 x 4 = 5 x 4.

20 = 20.

Therefore the product is 20.

Question 16.

6 × × 3 = ___

Answer:

The object = 2

6 x 2 x 3.

Using the associative property of multiplication.

(6 x 2) x 3 = 6 x (2 x 3)

12 x 3 = 6 x 6

36 = 36.

Therefore the product is 36.

Question 17.

× 3 × = _____

Answer:

Given that,

Smiley = 3.

Star = 4.

3 x 3 x 4.

Using the associative property of multiplication.

3 x (3 x 4) = (3 x 3) x 4.

3 x 12 = 9 x 4.

36 = 36.

Therefore the product is 36.

**Algebra Find the unknown number.**

Question 18.

4 × × 1 = 12

= ____

Answer:

4 x 1 = 12.

4 = 12.

12/4 = 3.

So, 4 x 3 x 1 = 12.

Using the associative property.

4 x (3 x 1) = (4 x 3) x 1

4 x 3 = 12 x 1

12 = 12.

Therefore the product is 12.

The unknown is 3.

Question 19.

2 × 5 × = 60

= ____

Answer:

2 x 5 = 60.

10 = 60.

60/10 = 6.

2 x 5 x 6 = 60.

Using the associative property of multiplication.

2 x (5 x 6) = (2 x 5) x 6

2 x 30 = 10 x 6.

60 = 60.

The product = 60.

The unknown = 6.

Question 20.

× 3 × 4 = 24

= ____

Answer:

3 x 4 = 24.

12 = 24.

24/12 = 2.

So, 2 x 3 x 4 = 24.

2 x (3 x 4) = (2 x 3) x 4

2 x 12 = 6 x 4.

24 = 24.

The product is 24.

The unknown is 2.

**Problem Solving**

**Write a number sentence to solve.**

Question 21.

Gabriel is training for a race. On days that he jogs, he jogs 2 miles. His exercise schedule is shown. How many miles will he jog in 6 weeks?

Answer:

Given that,

He jogs 2 miles on day.

He jogs on Monday, Tuesday, Thursday, Saturday.

The number of days are 4.

The number of weeks are 6.

So, 2 x 4 x 6

Using the commutative property of multiplication.

(2 x 4) x 6 = 2 x (4 x 6)

8 x 6 = 2 x 24

48 = 48

Therefore Gabriel jogs 48 miles.

Question 22.

**Mathematical PRACTICE 4 Model Math** Bianca bikes 2 miles to her grandfather’s house and 2 miles back to her house 5 times each month. How many miles does she bike each month?

Answer:

Given that,

Bianca bikes 2 miles to her grandfather’s house.

And 2 miles back to her house 5 times each month.

So, the number of miles in each month is 2 x 2 x 5.

Using the associative property of multiplication

(2 x 2) x 5 = 2 x (2 x 5)

4 x 5 = 2 x 10.

20 = 20.

Therefore the numbers of miles in each month she bike is 20.

**HOT Problems**

Question 23.

**Mathematical Practice 2 Reason** Circle the equation that does not belong with the other three. Explain.

4 × × 7 = 56 5 × 2 × = 40 × 3 × 9 = 54 4 × × 5 = 40

Answer:

4 x 2 x 7 = 56.

4 x (2 x 7) = (4 x 2) x 7

5 x 2 x 4 = 40.

5 x (2 x 4) = (5 x 2) x 4

2 x 3 x 9 = 54.

2 x (3 x 9) = (2 x 3) x 9

4 x 2 x 5 = 40.

4 x (2 x 5) = (4 x 2) x 5

Among the four equations 2 x 3 x 9 = 54 is different

So, circle the equation 2 x 3 x 9.

Question 24.

**? Building on the Essential Question** How does the Associative Property of Multiplication help you to calculate products mentally?

Answer:

In the associative property of multiplication in which way we multiply the factors in group we get the same product.

Suppose we have 2 x 3 x 4.

First multiply 2 x 3 = 6

Then multiply 6 x 4 = 24.

or

First multiply (3 x 4)

3 x 4 = 12.

Then Multiply 12 x 2 = 24.

In which way we can multiply you get the same product.

### McGraw Hill My Math Grade 4 Chapter 3 Lesson 6 My Homework Answer Key

**Practice**

**Multiply. Use the Associative Property.**

Question 1.

5 × 2 × 7 = ____

Answer:

Using the associative property of multiplication

(5 x 2) x 7 = 5 x (2 x 7)

10 x 7 = 5 x 14.

70 = 70.

Therefore the product is 70.

Question 2.

8 × 3 × 2 = ____

Answer:

Using the associative property of multiplication.

8 x (3 x 2) = (8 x 3) x 2.

8 x 6 = 24 x 2

48 = 48.

Therefore the product is 48.

Question 3.

4 × 2 × 5 = ____

Answer:

Using the associative property of multiplication.

4 x (2 x 5) = (4 x 2) x 5

4 x 10 = 8 x 5

40 = 40.

Therefore the product is 40.

**Algebra Find the unknown in each equation.**

Question 7.

4 × ___ × 8 = 64

Answer:

4 x 8 = 64.

32 = 64

64/32 = 2.

So, 4 x 2 x 8 = 64.

Therefore the unknown is 2.

Question 8.

3 × 4 × ____ = 120

Answer:

3 x 4 = 120.

12 = 120.

120/12 = 10.

3 x 4 x 10 = 120.

Therefore the unknown is 120.

Question 9.

4 × 2 × ____ = 40

Answer:

4 x 2 = 40.

8 = 40.

40/8 = 5.

So, 4 x 2 x 5 = 40.

Therefore the unknown is 5.

Question 10.

6 × 2 × ___ = 96

Answer:

6 x 2 = 96.

12 = 96

96/12 = 8.

So, 6 x 2 x 8 = 96.

Therefore the unknown is 8.

**Problem Solving**

**Mathematical PRACTICE 2 Use Algebra Write an equation to solve.**

Question 11.

A bus seats 4 people in a row, and there are 12 rows. How many people would fit on 2 buses?

Answer:

Given that,

A bus seats 4 people in a row.

The number of rows are 12.

The number of buses are 2.

So, the number of people are 4 x 12 x 2 = 96.

Therefore the number of people fit on 2 buses is 96.

Question 12.

Lucy’s pet snake eats 2 mice twice a week. How many mice will the snake eat in 6 weeks?

Answer:

Given that,

Lucy’s pet snake eats 2 mice twice a week.

Number of weeks equal to 6.

So, the number of mice is 2 x 2 x 6 = 24.

Therefore the Lucy’s pet snake eat 24 mice in 6 weeks.

Question 13.

Tyler delivers newspapers. He collected $10 from each customer. He has 5 customers on each street, and he delivers to 4 different streets. How much money did Tyler collect?

Answer:

Given that,

He collected $10 from each customer.

He has 5 customers on each street, and he delivers to 4 different streets.

So, Tyler collects is $10 x 5 x 4 = $10 x 20 = $200.

Therefore Tyler collects $200.

**Vocabulary Check**

**Draw a line to match each property with the equation that represents it.**

Answer:

**Test Practice**

Question 16.

Emerson runs 2 miles to her friend’s house and 2 miles back to her house 5 times each month. How many miles does she run?

A. 9 miles

B. 10 miles

C. 20 miles

D. 50 miles

Answer:

Given that,

Emerson runs 2 miles to her friend’s house.

Emerson runs 2 miles back to her house 5 times each month.

So, the number of miles that she run is 2 x 2 x 5 = 20.

Therefore she runs 20 miles.

Option C is the correct answer.