Solved Examples and Worksheet for Exploring Associative Property of Multiplication

Q1Name the property illustrated by the given equation.
4 × (2 × 1) = (4 × 2) × 1

A. commutative property of multiplication
B. associative property of addition
C. associative property of multiplication
D. commutative property of addition

Solutions
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Step: 1
4 × (2 × 1), (4 × 2) × 1 illustrates same product. But grouping of factors is changed.
Step: 2
According to associative property of multiplication, changing the grouping of factors does not change the product.
Step: 3
So, 4 × (2 × 1) = (4 × 2) × 1 illustrates associative property of multiplication.
Correct Answer is :   associative property of multiplication
Q2Use the associative property of multiplication to find the number sentence in such a way that the answer remains the same.
(1 × 2) × 4 = _______
A. 1 × (2 × 4)
B. 2 × 1
C. 1 × 4
D. 4 × (1 × 1)

Solutions
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Step: 1
The product of the expression (1 × 2) × 4 is (2) × 4 = 8.
  [Multiply.]
Step: 2
The associative property of multiplication states that "Changing the grouping of factors does not change the product."
Step: 3
So, (1 × 2) × 4 = 1 × (2 × 4) = 8.
  [Use the associative property of multiplication.]
Correct Answer is :   1 × (2 × 4)
Q3If 3 × (5 × 7) = 105, then find the value of (3 × 5) × 7.
A. 15
B. 56
C. 105
D. 8

Solutions
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Step: 1
The value of the expression 3 × (5 × 7) is 105.
Step: 2
The associative property of multiplication states that "Changing the grouping of factors does not change the product."
Step: 3
So, the value of (3 × 5) × 7 is 105.
Correct Answer is :   105
Q4If 5 × (8 × 11) = 440, then find the value of (5 × 8) × 11.
A. 13
B. 143
C. 24
D. 440

Solutions
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Step: 1
The value of the expression 5 × (8 × 11) is 440.
Step: 2
The associative property of multiplication states that "Changing the grouping of factors does not change the product.
Step: 3
So, the value of (5 × 8) × 11 is 440.
Correct Answer is :   440
Q5If 2 × (4 × 6) = 48, then find the value of (2 × 4) × 6.
A. 12
B. 36
C. 6
D. 48

Solutions
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Step: 1
The value of the expression 2 × (4 × 6) is 48.
Step: 2
The associative property of multiplication states that "Changing the grouping of factors does not change the product."
Step: 3
So, the value of (2 × 4) × 6 is 48.
Correct Answer is :   48
Q6Choose an expression that would give you the same product as 2 × (3 × 10).
A. (2 × 3) × 10
B. (2 + 3) × 10
C. (2 × 3) + 10
D. 2 + 3 + 10

Solutions
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Step: 1
The associative property of multiplication states that "Changing the grouping of factors does not change the product."
Step: 2
The value of the expression 2 × (3 × 10) is 60.
Step: 3
The value of (2 × 3) × 10 is 60.
  [Associative property of multiplication.]
Step: 4
So, the expression that would give the same product as 2 × (3 × 10) is (2 × 3) × 10.
Correct Answer is :   (2 × 3) × 10
Q7Name the property illustrated by the equation.
5 × (4 × 3) = (5 × 4) × 3
A. Commutative property of addition
B. Associative property of multiplication
C. Associative property of addition
D. Commutative property of multiplication

Solutions
Share 
Step: 1
5 × (4 × 3), (5 × 4) × 3 illustrates same product. But grouping of factors is changed.
Step: 2
According to associative property of multiplication, changing the grouping of factors does not change the product.
Step: 3
So, 5 × (4 × 3) = (5 × 4) × 3 illustrates associative property of multiplication.
Correct Answer is :   Associative property of multiplication
Q8Choose an expression that would give you the same product as 3 × (5 × 6).
A. (3 × 5) + 6
B. (3 × 5) × 6
C. 3 + 5 + 6

Solutions
Share 
Step: 1
The associative property of multiplication states that "Changing the grouping of factors does not change the product."
Step: 2
The value of the expression 3 × (5 × 6) is 90.
Step: 3
The value of (3 × 5) × 6 is 90.
  [Associative property of multiplication.]
Step: 4
So, the expression that would give the same product as 3 × (5 × 6) is (3 × 5) × 6.
Correct Answer is :   (3 × 5) × 6
Q9Choose an expression that would give you the same product as 3 × (8 × 7).

A. (3 + 8) × 7
B. (3 × 8) + 7
C. (3 × 8) × 7
D. 3 + 8 + 7

Solutions
Share 
Step: 1
The associative property of multiplication states that "Changing the grouping of factors does not change the product."
Step: 2
The value of the expression 3 × (8 × 7) is 168.
Step: 3
The value of (3 × 8) × 7 is 168.
  [Associative property of multiplication.]
Step: 4
So, the expression that would give the same product as 3 × (8 × 7) is (3 × 8) × 7.
Correct Answer is :   (3 × 8) × 7
Q10If 4 × (2 × 5) = 40, then find the value of (4 × 2) × 5.

A. 50
B. 30
C. 40
D. 34

Solutions
Share 
Step: 1
The value of the expression 4 × (2 × 5) is 40.
Step: 2
The associative property of multiplication states that "Changing the grouping of factors does not change the product."
Step: 3
So, the value of (4 × 2) × 5 is 40.
Correct Answer is :   40
Q11If 7 × (2 × 3) = 42, then find the value of (7 × 2) × 3.

A. 36
B. 42
C. 45
D. 24

Solutions
Share 
Step: 1
The value of the expression 7 × (2 × 3) is 42.
Step: 2
The associative property of multiplication states that "Changing the grouping of factors does not change the product."
Step: 3
So, the value of (7 × 2) × 3 is 42.
Correct Answer is :   42

HighSchool Math