# DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION 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 + z2)

Problem 5 :

Evaluate using distributive property :

m(m2 + m + 5)

Problem 6 :

Write the given verbal phrase into algebraic expression

"3 times the sum of two different numbers"

Problem 7 :

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

Problem 8 :

Write the given verbal phrase into algebraic expression :

"6 times the sum of three different numbers"

Problem 9 :

If 7 times the sum of 3 times of a number and 6 is 147, find the number.

Problem 10 :

If 9 times the sum of 7 and 4 times of a number is 135, 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)  =  84

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 + z2)

Solution :

Use distributive property.

5(x2 + y2 + z2)  =  5x2 + 5y2 + 5z2

Problem 5 :

Evaluate using distributive property :

m(m2 + m + 5)

Solution :

Use distributive property.

m(m2 + m + 5)  =  m ⋅ m2 + m ⋅ m + 5m

m(m2 + m + 5)  =  m3 + m2 + 5m

Problem 6 :

Write the given verbal phrase into algebraic expression

"3 times the sum of two different numbers"

Solution :

Let x and y be the two different numbers.

Then, 3 times the sum of two different numbers is

=  3(x + y)

Use distributive property.

=  3x + 3y

Problem 7 :

If 4 times the sum 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

Subtract 20 from  each side.

4x  =  12

Divide each side by 4.

x  =  3

So, the number is 3.

Problem 8 :

Write the given verbal phrase into algebraic expression :

"6 times the sum of three different numbers"

Solution :

Let x, y and z be the three different numbers.

Then, 6 times the um of three different numbers is

=  6(x + y + z)

Use distributive property.

=  6x + 6y + 6z

Problem 9 :

If 7 times the sum of 3 times of a number and 6 is 147, find the number.

Solution :

Let x be the number.

Then,

7(3x + 6)  =  147

Use distributive property.

21x + 42  =  147

Subtract 42 from each side.

21x  =  105

Divide each side by 21.

x  =  5

So, the number is 5.

Problem 10 :

If 9 times the sum of 7 and 4 times of a number is 135, find the number.

Solution :

Let x be the number.

Then,

9(7 + 4x)  =  135

Use distributive property.

63 + 36x  =  135

Subtract 63 from each side.

36x  =  72

Divide each side by 36.

x  =  2

So, the number is 2.

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