# 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.

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

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

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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