Solved Examples and Worksheet for Using Distributive Property to Solve Problems

Q1Identify the equation which satisfies distributive property.

A. 4(x - 4) = x - 16
B. 4(x - 4) = 4x + 16
C. 4(x - 4) = 4x - 16
D. 4(x - 4) = x + 16

Solutions
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Step: 1
Distributive property states that the product of a number and a sum is equal to the sum of the individual products of addends and the number. a(b + c) = ab + ac.
Step: 2
From the given choices "4(x - 4) = 4x - 16" satisfies distributive property.
Correct Answer is :   4(x - 4) = 4x - 16
Q2Use the distributive property to rewrite: 3(x - 4)
A. x + 12
B. 3x + 12
C. x - 12
D. 3x - 12

Solutions
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Step: 1
3(x - 4)
  [Given expression.]
Step: 2
= 3 × x - 3 × 4
  [Distributive property.]
Step: 3
= 3x - 12
Correct Answer is :   3x - 12
Q3Identify the equation which satisfies distributive property.
A. 4(x - 3) = x + 12
B. 4(x - 3) = 4x + 12
C. 4(x - 3) = x - 12
D. 4(x - 3) = 4x - 12

Solutions
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Step: 1
Distributive property states that the product of a number and a sum is equal to the sum of the individual products of addends and the number. a(b + c) = ab + ac.
Step: 2
From the given choices " 4(x - 3) = 4x - 12" satisfies distributive property.
Correct Answer is :   4(x - 3) = 4x - 12
Q4Which property is illustrated in the equation below?
2(p + 4) = 2p + 8
A. Additive Identity Property
B. Distributive Property
C. Associative Property of Addition
D. Commutative Property of Addition

Solutions
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Step: 1
2(p + 4) = 2p + 8
  [Given expression.]
Step: 2
In the expression the product of a number and a sum is same as the sum of the individual products of addends and the number.
Step: 3
Distributive property states that the product of a number and a sum is equal to the sum of the individual products of addends and the number.
Step: 4
So, the property 'Distrubitive Property' is illustrated in the given equation.
Correct Answer is :   Distributive Property
Q5Andrea wanted to find the area of the large rectangle ABFE. She used the distributive property to solve the area of the rectangle ABFE. Which of the methods shows Andrea′s steps?


A. Method 3
B. Method 4
C. Method 1
D. Method 2

Solutions
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Step: 1
Distributive property states that the product of a number and a sum is equal to the sum of the individual products of addends and the number.
Step: 2
Among the methods, Method 2 illustrates the sum of individual products of addends and the number.
  [Given that Andrea used distributive property to solve the area of the rectangle ABFE.]
Step: 3
So, Method 2 shows Andrea's steps.
Correct Answer is :   Method 2
Q6John′s drawing room measures 14 ft by 10512 ft. Which of the following he would use to find the area of the dining room using the distributive property?
A. (14 × 10) + (14 × 512)
B. 14 + 10 × 512
C. 14 × 12512
D. 14 × 10 + 512

Solutions
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Step: 1
Area of the room = length × width = 14 × 10512
Step: 2
14 × 10512 = 14(10 + 512)
  [10512can be written as 10 + 512]
Step: 3
= (14 × 10) + (14 × 512)
  [Using distributive property.]
Step: 4
Using distributive property we can write 14 × 10512 as (14 × 10) + (14 × 512).
Correct Answer is :    (14 × 10) + (14 × 512)
Q7Identify the expression that is the same as 4(5 + 6).

A. (4 × 5) + (4 × 6)
B. 4 × 5 + 6
C. (4 + 5)6
D. 4 × 5 × 6

Solutions
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Step: 1
Distributive property is a(b + c) = (a × b) + (a × c), where a, b and c are numbers.
Step: 2
So, 4(5 + 6) = (4 × 5) + (4 × 6).
Correct Answer is :   (4 × 5) + (4 × 6)
Q8Which of the following is the same as 23(179 + 235)?

A. (23 × 179) + (23 × 235)
B. (23 + 179) 235
C. (23 + 179) × (23 + 235)
D. (23 + 235) 179

Solutions
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Step: 1
Distributive property is a(b + c) = (a × b) + (a × c), where a, b and c are numbers.
Step: 2
= (23 × 179) + (23 × 235)
Correct Answer is :   (23 × 179) + (23 × 235)
Q9Which of the following is true?
A. 9(7 + 4) = (9 + 7)4
B. 9(7 + 4) = 9 × 7 × 4
C. 9(7 + 4) = 9 × 7 + 9 × 4
D. 9(7 + 4) = 9 × 7 + 4

Solutions
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Step: 1
a(b + c) = a × b + a × c
  [Distributive property.]
Step: 2
So, 9(7 + 4) = 9 × 7 + 9 × 4
Correct Answer is :   9(7 + 4) = 9 × 7 + 9 × 4
Q10George's lawn measures 16 ft by 1212ft. Which of the following would he use to find the area of the lawn using distributive property?
A. 16 × 12 + 12
B. 16 × 12
C. 16 + 12 × 12
D. (16 × 12) + (16 × 12)

Solutions
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Step: 1
Area of George's lawn = length × width = 16 × 1212
Step: 2
16 × 1212 = 16(12 + 12)
Step: 3
= (16 × 12) + (16 × 12)
  [Using distributive property.]
Step: 4
Using distributive property we can write 16 × 1212 as (16 × 12) + (16 × 12).
Correct Answer is :   (16 × 12) + (16 × 12)

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