DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER SUBTRACTION WORKSHEET

Problem 1 : 

Evaluate using distributive property :

7(10 - 2)

Problem 2 : 

Evaluate using distributive property :

6(x - y)

Problem 3 : 

Evaluate using distributive property :

m(n - p)

Problem 4 : 

Evaluate using distributive property :

5(x2 - y2)

Problem 5 : 

Evaluate using distributive property :

m(m2 - m)

Problem 6 : 

Write the given verbal phrase into algebraic expression

"3 times the difference of two different numbers"

Problem 7 : 

If 4 times the difference of a number and 5 is 32, find the number. 

Problem 8 : 

Write the given verbal phrase into algebraic expression

"6 times 3 less than 4 times of a number"

Problem 9 : 

If 7 times 6 less than 3 times of a number is 147, find the number. 

Problem 10 : 

If 9 times the difference of 7 and 4 times of a number is 27, find the number. 

Detailed Answer Key

Problem 1 : 

Evaluate using distributive property :

7(10 - 2)

Solution :

Use distributive property.

7(10 - 2)  =  7(10) - 7(2)

7(10 - 2)  =  70 - 14 

7(10 - 2)  =  56

Problem 2 : 

Evaluate using distributive property :

6(x - y)

Solution :

Use distributive property.

6(x - y)  =  6x - 6y

Problem 3 : 

Evaluate using distributive property :

m(n - p)

Solution :

Use distributive property.

m(n - p)  =  mn - mp

Problem 4 : 

Evaluate using distributive property :

5(x2 - y2)

Solution :

Use distributive property.

5(x2 - y2)  =  5x2 - 5y2

Problem 5 : 

Evaluate using distributive property :

m(m2 - m)

Solution :

Use distributive property.

m(m2 - m)  =  m ⋅ m2 - m ⋅ m

m(m2 - m)  =  m3 - m2

Problem 6 : 

Write the given verbal phrase into algebraic expression

"3 times the difference of two different numbers"

Solution :

Let x and y be the two different numbers.

Then, 3 times the difference of two different numbers is 

=  3(x - y)

Use distributive property.

=  3x - 3y

Problem 7 : 

If 4 times the difference of a number and 5 is 32, find the number. 

Solution :

Let x be the number. 

Then,

4(x - 5)  =  32

Use distributive property. 

4x - 20  =  32

Add 20 to each side. 

4x  =  52

Divide each side by 4.

x  =  13

So, the number is 13. 

Problem 8 : 

Write the given verbal phrase into algebraic expression

"6 times 3 less than 4 times of a number"

Solution :

Let x be the number.

Then, 6 times 3 less than 4 times a number is 

=  6(4x - 3)

Use distributive property.

=  24x - 12

Problem 9 : 

If 7 times 6 less than 3 times of a number is 147, find the number. 

Solution :

Let x be the number. 

Then,

7(3x - 6)  =  147

Use distributive property.

21x - 42  =  147

Add 42 to each side. 

21x  =  189

Divide each side by 21.

x  =  9

So, the number is 9. 

Problem 10 : 

If 9 times the difference of 7 and 4 times of a number is 27, find the number. 

Solution :

Let x be the number. 

Then, 

9(7 - 4x)  =  27

Use distributive property.

63 - 36x  =  27

Subtract 63 from each side. 

-36x  =  -36

Divide each side by (-36).

x  =  1

So, the number is 1. 

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