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

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.

Use repeated addition to find 12 × 3. ____
12 + 12 + 12 =
=
Another Way
Multiply 6 × 3 first.

Use repeated addition to find 18 × 2.
18 + 18 =
=
So, Raul will have ____ video games.

There are 2 video games in each value pack.
There are 6 value packs in each box.
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.

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

Parentheses () tell you which numbers to multiply first

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

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.

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.

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.

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 = ____
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 = ____
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 = ___
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 = ____
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 = ____
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 = ___
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 = ____
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 = ____
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 = ____
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
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
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 × = ____
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 = ___
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 × = _____
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
= ____
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
= ____
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
= ____
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?

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?

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
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?
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 = ____
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 = ____
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 = ____
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
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
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
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
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?
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?
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.

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