All the solutions provided in McGraw Hill My Math Grade 3 Answer Key PDF Chapter 9 Lesson 4 The Associative Property will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 3 Answer Key Chapter 9 Lesson 4 The Associative Property
The Associative Property of Multiplication states that the grouping of factors does not change the product.
Math in My World
Example 1
Chris and Katie each received 4 smile stickers a week for 3 weeks. How many smile stickers did they earn altogether?
Find the unknown in 2 Ă— 3 Ă— 4 = ____________.
When there are no parentheses, multiply in order from left to right. Or, use parentheses to group factors.
One Way
Multiply 2 and 3 first.
The unknown is 24.
Another Way:
Multiply 3 and 4 first.
The unknown is 24.
Helpful Hint
The Associative Property also allows you to group the easier factors.
Either way 2 Ă— 3 Ă— 4 = _______________.
The _______________ Property shows that grouping does not change the product.
Answer: The Associative Property Property shows that grouping does not change the product.
Explanation:
Given, 2 Ă— 3 Ă— 4
( 2 Ă— 3 ) Ă— 4
Multiply the factors inside the parentheses first.
6 Ă— 3Â = 24
So, 2 Ă— ( 3 Ă— 4 ) = 24
So, The Associative Property Property shows that grouping does not change the product.
Example 2
Cheryl has 2 photos. Each photo shows 5 friends holding the same number of flowers. There are 30 flowers altogether. How many flowers is each friend holding?
Write a multiplication sentence to help you find the missing factor.
So, 2 Ă— 5 Ă— 3 = ______________. Each friend is holding _____________ flowers.
Answer: 2 Ă— 5 Ă— 3 = 30 , Each friend is holding 30 flowers
Explanation:
Given, ( 2 Ă— 5 ) Ă— 3
Multiply the factors inside the parentheses first.
10 Ă— 3Â = 30
So, 2 Ă— ( 5 Ă— 3 ) = 30.
Hence, Each friend is holding 30 flowers.
Talk Math
Explain how the Associative Property of Multiplication can help you find missing factors.
Answer: The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.
Explanation:
For example, 7 Ă—(2 Ă— 3) = (7 Ă— 2) Ă— 3 = 42.
So, The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.
Guided PracticeÂ
Use parentheses to group two factors. Then find each product.
Question 1.
Answer:
Explanation:
Given, 2 Ă— 4 Ă— 6
( 2 Ă— 4 ) Ă—6
Multiply the factors inside the parentheses first.
8 Ă— 6Â = 48
So, 2 Ă— ( 4 Ă— 6 ) = 48.
Question 2.
Answer:
Explanation:
Given, 2 Ă— 4 Ă— 3
( 2 Ă— 4 ) Ă— 3
Multiply the factors inside the parentheses first.
8 Ă— 3Â = 24
So, 2 Ă— ( 4 Ă— 3 ) = 24.
Question 3.
Algebra Find the missing factor.
So, the unknown is ______________.
Answer: The unknown is 5
Explanation:
Given, ? Ă— 2 Ă— 3
( ? Ă— 2 ) Ă— 3
Let the unknown be 5
Multiply the factors inside the parentheses first.
5 Ă— 2 Ă— 3Â = 30
So, 5 Ă— ( 2 Ă— 3 ) = 30.
Thus, The unknown is 5
Independent Practice
Use parentheses to group two factors. Then find each product.
Question 4.
Answer:
Explanation:
Given,4 Ă— 1 Ă— 3
(4 Ă— 1 ) Ă— 3
Multiply the factors inside the parentheses first.
4 Ă— 3Â = 12
So, 4 Ă— ( 1 Ă— 3 ) = 12.
Question 5.
Answer:
Explanation:
Given, 2 Ă— 3 Ă— 3
( 2 Ă— 3 ) Ă— 3
Multiply the factors inside the parentheses first.
6 Ă— 3Â = 18
So, 2 Ă— ( 3 Ă— 3 ) = 18.
Question 6.
6 Ă— 2 Ă— 2 = _____________
Answer: 6 Ă— 2 Ă— 2 = 24
Explanation:
Given, 6 Ă— 2 Ă— 2
( 6 Ă— 2 ) Ă— 2
Multiply the factors inside the parentheses first.
12 Ă— 2Â = 24
So, 6 Ă— ( 2 Ă— 2 ) = 24.
Question 7.
2 Ă— 3 Ă— 2 = ______________
Answer: 2 Ă— 3 Ă— 2 =12
Explanation:
Given, 2 Ă— 3 Ă— 2
( 2 Ă— 3 ) Ă— 2
Multiply the factors inside the parentheses first.
6 Ă— 2Â = 12
So, 2 Ă— (3 Ă— 2 ) = 12.
Algebra Find each missing factor.
Question 8.
(3 Ă— ) Ă— 4 = 24
The unknown is ____________.
Answer: The unknown is 2
Explanation:
Given, (3 Ă— ) Ă— 4 = 24
Let the unknown be y
3 Ă— y Ă— 4 = 24
y = \(\frac{24}{4 Ă— 3}\)
y = 2
So, The unknown is 2.
Question 9.
(6 Ă— ) Ă— 5 = 30
The unknown is ____________.
Answer: The unknown is 1
Explanation:
Given, (6 Ă— ) Ă— 5 = 30
Let the unknown be y
6 Ă— y Ă— 5 = 30
y = \(\frac{30}{6 Ă— 5}\)
y = 1
So, The unknown is 1.
Question 10.
Ă— (3 Ă— 3) = 27
The unknown is ____________.
Answer: The unknown is 3.
Explanation:
Given, Ă— (3 Ă— 3) = 27
Let the unknown be y
y Ă— 3 Ă— 3 = 27
y = \(\frac{27}{3 Ă— 3}\)
y = 3
So, The unknown is 3.
Question 11.
(2 Ă— 5) Ă— = 20
The unknown is ____________.
Answer: The unknown is 2
Explanation:
Given, (2 Ă— 5) Ă— = 20
Let the unknown be y
2 Ă— 5 Ă— y = 20
y = \(\frac{20}{2 Ă— 5}\)
y = 2
So, The unknown is 2.
Algebra Find the value of each number sentence.
Question 12.
(6 Ă— 1) Ă— = ______________
Answer: (6 Ă— 1) Ă— 2 =12
Explanation:
Given, figure value is 2
Then, (6 Ă— 1) Ă— 2
Multiply the factors inside the parentheses first.
6 Ă— 2Â = 12
So, 6 Ă— ( 1 Ă—2 ) = 12.
Question 13.
4 Ă— ( Ă— 2) = ______________
Answer: 4 Ă— ( 3 Ă— 2 ) = 24.
Explanation:
Given, figure value is 3
Then, ( 4 Ă— 3 ) Ă— 2
Multiply the factors inside the parentheses first.
12 Ă— 3Â = 24
So, 4 Ă— ( 3 Ă— 2 ) = 24.
Question 14.
Ă— ( Ă— 5) = _____________
Answer: 4 Ă— ( 2 Ă— 5 ) = 40.
Explanation:
Given, figure value is 4 and 2
Then, ( 4 Ă— 2 ) Ă— 5
Multiply the factors inside the parentheses first.
8 Ă— 5Â = 40
So, 4 Ă— ( 2 Ă— 5 ) = 40.
Question 15.
(6 Ă— ) Ă— 3 = _______________
Answer: 6 Ă— ( 2 Ă— 3 ) = 36.
Explanation:
Given, figure value is 2
Then, ( 6 Ă— 2 ) Ă— 3
Multiply the factors inside the parentheses first.
12 Ă— 3Â = 36
So, 6 Ă— ( 2 Ă— 3 ) = 36.
Question 16.
Ă— (3 Ă— ) = _______________
Answer: 3 Ă— ( 3 Ă— 4 ) = 36.
Explanation:
Given, figure value is 3 and 4
Then, ( 3 Ă— 3 ) Ă—4
Multiply the factors inside the parentheses first.
9 Ă— 4Â = 36
So, 3 Ă— ( 3 Ă— 4 ) = 36.
Question 17.
(5 Ă— ) Ă— = ______________
Answer: 5 Ă— ( 2 Ă— 3 ) = 36.
Explanation:
Given, figure value is 2 and 3
Then, ( 5 Ă— 2 ) Ă—3
Multiply the factors inside the parentheses first.
10 Ă— 3Â = 30
So, 5 Ă— ( 2 Ă— 3 ) = 36.
Problem Solving
Question 18.
Mathematical PRACTICE Make a Plan There are 5 apples. Troy cuts each apple into 2 pieces. Beth cuts each piece into 4 slices. What is the total number of apple slices?
Answer: There are 40 apple slices
Explanation:
Given, There are 5 apples. Troy cuts each apple into 2 pieces.
Beth cuts each piece into 4 slices.
That makes, 5 Ă— ( 2 Ă— 4 )
Multiply the factors inside the parentheses first.
10 Ă— 4Â = 40
So, 5 Ă— ( 2 Ă— 4 ) = 40
Hence, There are 40 apple slices.
Question 19.
Troy and Beth each cut 2 bananas into 4 pieces. What is the total number of banana pieces?
Answer: There are 16 banana pieces
Explanation:
Given, Troy and Beth each cut 2 bananas into 4 pieces.
That makes, 2 Ă— 2 Ă— 4
Multiply the factors inside the parentheses first.
4 Ă—4Â = 16
So, 2 Ă— ( 2 Ă— 4 ) = 16.
Question 20.
A clerk unpacked 2 boxes of nails. Each box held 4 cartons with 10 packages of nails. How many packages of nails did the clerk unpack?
Answer: Clerk unpacked 80 packages of nails
Explanation:
Given, A clerk unpacked 2 boxes of nails. Each box held 4 cartons with 10 packages of nails.
That makes, 2 Ă— ( 4 Ă— 10 )
Multiply the factors inside the parentheses first.
8 Ă— 10Â = 80
So, 2 Ă— ( 4 Ă— 10 ) = 80.
Hence, Clerk unpacked 80 packages of nails.
HOT Problems
Question 21.
Mathematical PRACTICE Find the Error From the following, circle the number sentence that is not true. Explain.
(2 Ă— 3) Ă— 3 = 2 Ă— (3 Ă— 3)
3 Ă— (1 Ă— 5) = (3 Ă— 1) Ă— 5
4 Ă— (4 Ă— 2) = (3 Ă— 4) Ă— 4
6 Ă— (4 Ă— 2) = (6 Ă— 4) Ă— 2
Answer: 4 Ă— (4 Ă— 2) = (3 Ă— 4) Ă— 4 is not true
Explanation:
From the given question,
4 Ă— (4 Ă— 2) = (3 Ă— 4) Ă— 4 is not true, because
Here, not only the factors are grouped together
but also the numbers are changed as 2 as 3
So, 4 Ă— (4 Ă— 2) = (3 Ă— 4) Ă— 4 is not true
Question 22.
Building on the Essential Question Explain why the grouping of the factors does not matter when finding (3 Ă— 4) Ă— 2.
Answer: 24, Either way the result of the product is same.
Explanation:
Given, (3 Ă— 4) Ă— 2.
(3 Ă— 4) Ă— 2.
Multiply the factors inside the parentheses first.
12 Ă— 2 = 24
or
3 Ă— (4 Ă— 2)
Group the same factors another way.
3 Ă— 8 = 24
Either way the result of the product is same.
McGraw Hill My Math Grade 3 Chapter 9 Lesson 4 My Homework Answer Key
Practice
Use parentheses to group two factors. Then find each product.
Question 1.
2 Ă— 3 Ă— 6 = ______________
Answer: 2 Ă— 3 Ă— 6 = 36
Explanation:
Given, 2 Ă— 3 Ă— 6
( 2 Ă— 3 ) Ă—6
Multiply the factors inside the parentheses first.
6 Ă— 6Â = 36
So, 2 Ă— ( 3 Ă— 6 ) = 36.
Question 2.
5 Ă— 2 Ă— 2 = ________________
Answer: 5 Ă— 2 Ă— 2 = 20
Explanation:
Given, 5 Ă— 2 Ă— 2
( 5 Ă— 2 ) Ă— 2
Multiply the factors inside the parentheses first.
10 Ă— 2Â = 20
So, 5 Ă— ( 2 Ă— 2 ) = 20.
Algebra Find each missing factor.
Question 3.
4 Ă— ( Ă— 4) = 32
The unknown is _____________.
Answer: The unknown is 2
Explanation:
Given, 4 Ă— ( Ă— 4) = 32
Let the unknown be y
4 Ă— y Ă— 4 = 32
y = \(\frac{32}{4 Ă— 4}\)
y = 2
So, The unknown is 2.
Question 4.
(2 Ă— ) Ă— 6 =60
The unknown is ______________.
Answer: The unknown is 5.
Explanation:
Given, (2 Ă— ) Ă— 6 =60
Let the unknown be y
2 Ă— y Ă— 6 = 60
y = \(\frac{60}{2 Ă— 6}\)
y =5
So, The unknown is 5.
Question 5.
(5 Ă— ) Ă— 1 = 45
The unknown is _____________.
Answer: The unknown is 9.
Explanation:
Given, (5 Ă— ) Ă— 1 = 45
Let the unknown be y
5 Ă— y Ă— 1 = 45
y = \(\frac{45}{5 Ă— 1}\)
y =9
So, The unknown is 9.
Question 6.
Ă— (4 Ă— 2) = 48
The unknown is _____________.
Answer: The unknown is 6.
Explanation:
Given, Ă— (4 Ă— 2) = 48
Let the unknown be y
4 Ă— y Ă— 2 = 48
y = \(\frac{48}{4 Ă— 2}\)
y = 6
So, The unknown is 6.
Problem Solving
Question 7.
Mathematical PRACTICE Use Number Sense Mariette bought 4 packs of sparkling water. There were 6 bottles in each pack. If each bottle cost $2, how much did Mariette spend on sparkling water?
Answer: Mariette spend $48 on sparkling water.
Explanation:
Given, Mariette bought 4 packs of sparkling water.
There were 6 bottles in each pack. If each bottle cost $2,
that makes, 4 Ă— ( 6 Ă— 2 )
Multiply the factors inside the parentheses first.
4 Ă— 12Â = 48
So, ( 4 Ă— 6 ) Ă— 2 =48.
Hence, Mariette spend $48 on sparkling water.
Question 8.
Jamal and Brianna each bought 3 oranges. They sliced each orange into 6 pieces. How many orange slices did Jamal and Brianna have altogether?
Answer: Jamal and Brianna have altogether 36 orange slices.
Explanation:
Given, Jamal and Brianna each bought 3 oranges.
They sliced each orange into 6 pieces.
That makes, 2 Ă— ( 3 Ă— 6 )
Multiply the factors inside the parentheses first.
6 Ă— 6Â = 36
So, ( 2 Ă— 3 ) Ă— 6 = 36.
Hence, Jamal and Brianna have altogether 36 orange slices.
Question 9.
Mr. and Mrs. Perry packed their lunch 5 days in a row. Each of them packed 3 oatmeal cookies for dessert every day. What is the total number of cookies they packed for lunch that week?
Answer: The total number of cookies they packed for lunch that week is 30.
Explanation:
Given, Mr. and Mrs. Perry packed their lunch 5 days in a row.
Each of them packed 3 oatmeal cookies for dessert every day.
That makes, 2 Ă— ( 5 Ă— 3 )
Multiply the factors inside the parentheses first.
2 Ă— 15Â = 30
So, ( 2 Ă— 5 ) Ă— 3 = 30.
Hence, The total number of cookies they packed for lunch that week is 30.
Vocabulary Check
Question 10.
Write a definition for the Associative Property of Multiplication.
Answer: The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.
Explanation:
For Example, ( 5 × 4 ) × 2 or 5 × ( 4 × 2 ).
Test Practice
Question 11.
What is the unknown in (3 Ă— 3) Ă— 7 =
(A) 21
(B) 30
(C) 42
(D) 63
Answer: D
Explanation:
Given, (3 Ă— 3) Ă— 7
Multiply the factors inside the parentheses first.
9 Ă— 7Â = 63
So, 3 Ă— ( 3 Ă— 7 ) = 63.
Hence, option D is correct.