Solved Examples and Worksheet for Distributive Property of Multiplication over Addition

Q1Which statement is equivalent to 7 × 52?

A. (7 × 5) + (7 × 2)
B. (7 × 50) + (7 × 2)
C. 5 × 72
D. (7 × 49) - (7 × 3)

Solutions
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Step: 1
7 × 52
  [Original expression.]
Step: 2
= 7 × (50 + 2)
  [Rewrite 52 as sum of 50 and 2.]
Step: 3
= 7 × 50 + 7 × 2
  [a × (b + c) = a × b + a × c by distributive property.]
Step: 4
Therefore, (7 × 50) + (7 × 2) is equivalent to 7 × 52.
Correct Answer is :   (7 × 50) + (7 × 2)
Q2Which statement is equivalent to 3 × 31?
A. (3 × 31) + (3 × 1)
B. (3 × 30) + (3 × 1)
C. (3 × 30) - (3 × 1)
D. 3 × 13

Solutions
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Step: 1
3 × 31
  [original expression.]
Step: 2
3 × (30 + 1)
  [Rewrite 31 as sum of 30 and 1.]
Step: 3
= 3 × 30 + 3 × 1
  [a × (b + c) = a × b + a × c by distributive property.]
Step: 4
Therefore, (3 × 30) + (3 × 1) is equivalent to 3 × 31.
Correct Answer is :   (3 × 30) + (3 × 1)
Q3Find the total number of items in the given figure by using the distributive property.


A. 48
B. 35
C. 38
D. 40

Solutions
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Step: 1
The number of items in each rectangle is the height times the width.
Step: 2
The items= (8 × 2) + (8 × 4)
  [So, instead of doing 2 separate multiplications, use distributive property.]
Step: 3
8 × (2 + 4)
  [Take out the common factor.]
Step: 4
8 × 6
  [Perform addition.]
Step: 5
= 48
  [Muliply.]
Correct Answer is :   48
Q4Find the total number of items in the given figure by using the distributive property.

A. 21
B. 25
C. 20
D. 28

Solutions
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Step: 1
The number of items in each rectangle is the height times the width.
Step: 2
The items= (3 × 5) + (3 × 2)
  [So, instead of doing 2 separate multiplications, use distributive property.]
Step: 3
= 3 × (5 + 2)
  [Take out the common factor.]
Step: 4
3 × 7
  [Perform addition.]
Step: 5
= 21
  [Multiply]
Correct Answer is :   21
Q5Find the total number of items in the given figure by using the distributive property.


A. 40
B. 42
C. 45
D. 48

Solutions
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Step: 1
The number of items in each rectangle is the height times the width.
Step: 2
The items= (6 × 2) + (6 × 5)
  [So, instead of doing 2 separate multiplications, use distributive property.]
Step: 3
6 × (2 + 5)
  [Take out the common factor.]
Step: 4
6 × 7
  [Perform addition.]
Step: 5
= 42
  [Multiply.]
Correct Answer is :   42
Q6Find the total number of items in the given figure by using the distributive property.


A. 35
B. 48
C. 40
D. 38

Solutions
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Step: 1
The number of items in each rectangle is the height times the width.
Step: 2
The items= (7 × 4) + (7 × 2)
  [So, instead of doing 2 separate multiplications, use distributive property.]
Step: 3
7 × (4 +2)
  [Take out the common factor.]
Step: 4
= 7 × 6
  [Perform addition.]
Step: 5
= 42
  [Multiply.]
Correct Answer is :   48
Q7Find the total number of items in the given figure by using the distributive property.


A. 30
B. 40
C. 45
D. 35

Solutions
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Step: 1
The number of items in each rectangle is the height times the width.
Step: 2
The items= (5 × 4) + (5 × 3)
  [So, instead of doing 2 separate multiplications, use distributive property.]
Step: 3
= 5 × (4 + 3)
  [Take out the common factor.]
Step: 4
= 5 × 7
  [Perform addition.]
Step: 5
= 35
  [Multiply.]
Correct Answer is :   35
Q8Find the total number of items in the given figure by using the distributive property.


A. 10
B. 18
C. 16
D. 15

Solutions
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Step: 1
The number of items in each rectangle is the height times the width.
Step: 2
The items= (2 × 5) + (2 × 3)
  [So, instead of doing 2 separate multiplications, use distributive property.]
Step: 3
= 2 × (5 + 3)
  [Take out the common factor.]
Step: 4
= 2 × 8
  [Perform addition.]
Step: 5
= 16
  [Multiply.]
Correct Answer is :   16
Q9Find the total number of items in the given figure by using the distributive property.


A. 48
B. 38
C. 35
D. 40

Solutions
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Step: 1
The number of items in each rectangle is the height times the width.
Step: 2
The items= (9 × 3) + (9 × 2)
  [So, instead of doing 2 separate multiplications, use distributive property.]
Step: 3
= 9 × (3 + 2)
  [Take out the common factor.]
Step: 4
= 9 × 5
  [Perform addition.]
Step: 5
= 45
  [Multiply.]
Correct Answer is :   48
Q10Which is equal to (4 × 11) + (4 × 9)?

A. 4 + (11 × 9)
B. 4 × (11 × 9)
C. 4 × (11 + 9)
D. 4 × (11 × 9)

Solutions
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Step: 1
(4 × 11) + (4 × 9)
  [Original expression.]
Step: 2
4 × (11 + 9)
  [Use distributive property.]
Correct Answer is :   4 × (11 + 9)
Q11Which is equal to (8 × 3) + (8 × 5)?

A. 8 × (3 × 5)
B. 8 × (3 × 5)
C. 8 + (3 × 5)
D. 8 × (3 + 5)

Solutions
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Step: 1
(8 × 3) + (8 × 5)
  [Original expression.]
Step: 2
= 8 × (3 + 5)
  [Use distributive property.]
Correct Answer is :   8 × (3 + 5)

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