USING THE DISTRIBUTIVE PROPERTY WORKSHEET

Problem 1 : 

Simplify the following expression : 

5 - 3(7x + 8)

Problem 2 : 

Simplify the following expression : 

(2/3)(6e + 9f -21g) - 7f

Problem 3 :

Solve for x :

4(x - 3) + 2  =  2 + x

Problem 4 :

Solve :

k/7 - 6  =  3k/7 + 4

Problem 5 :

Solve for n :

7n/10 + 3/2  =  3n/5 + 2

Problem 6 : 

James is selling tickets for a high school band concert. The band gets to keep 25% of the money he collects from ticket sales to put toward new uniforms. Write an expression to represent how much the band gets to keep.

Detailed Answer Key

Problem 1 : 

Simplify the following expression : 

5 - 3(7x + 8)

Solution : 

=  5 - 3(7x + 8)

Use the distributive property. 

=  5 - 3(7x) - 3(8)

Simplify. 

=  5 - 21x - 24

=  -21x - 19

Problem 2 : 

Simplify the following expression : 

(2/3)(6e + 9f -21g) - 7f

Solution : 

=  (2/3)(6e + 9f - 21g) - 7f

Use the distributive property. 

=  4e + 6f - 14g - 7f

Simplify. 

=  4e - f - 14g

Problem 3 :

Solve for x :

4(x - 3) + 2  =  2 + x

Solution :

4(x - 3) + 2  =  2 + x

Use the Distributive Property.

4x - 12 + 2  =  2 + x

Simplify 

4x - 10  =  2 + x

Subtract x from each side. 

3x - 10  =  2

Add 10 to each side. 

3x  =  12

Divide each side by 3.

x  =  4

Problem 4 :

Solve :

k/7 - 6  =  3k/7 + 4

Solution :

k/7 - 6  =  3k/7 + 4

Multiply both sides of the equation by 7 to get rid of the denominator 7.  

7(k/7 - 6)  =  7(3k/7 + 4)

Use distributive property.

7(k/7) - 7(6)  =  7(3k/7) + 7(4)

Simplify.

k - 42  =  3k + 28

Subtract k from both sides. 

-42  =  2k + 28

Subtract 28 from each side. 

-70  =  2k

Divide each side by 2. 

-70 / 2  =  2k / 2

-35  =  k

Problem 5 :

Solve for n :

7n/10 + 3/2  =  3n/5 + 2

Solution :

Step 1 :

Find the least common multiple of the denominators (10, 2 and 5).

LCM  =  5 x 2 x 1 x 1 x 1

LCM  =  10

Step 2 : 

Multiply both sides of the equation by 10 to get rid of the denominators. 

10(7n/10 + 3/2)  =  10(3n/5 + 2)

Use distributive property.

10(7n/10) + 10(3/2)  =  10(3n/5) + 10(2)

Simplify.

7n + 5(3)  =  2(3n) + 20

7n + 15  =  6n + 20

Subtract 6n from each side. 

n + 15  =  20

Subtract 15 from each side. 

n  =  5

Problem 6 : 

James is selling tickets for a high school band concert. The band gets to keep 25% of the money he collects from ticket sales to put toward new uniforms. Write an expression to represent how much the band gets to keep.

Solution : 

Let a represent the number of adult tickets he sells.

Let y represent the number of youth tickets he sells.

The expression 16.60a + 12.20y represents the amount of money James collects from ticket sales.

Write 25% as a decimal :

0.25

Write an expression to represent 25% of the money he collects :

0.25(16.60a + 12.20y)

That is, 25% adult ticket sales and youth ticket sales. 

Use the Distributive Property to simplify the expression.

=  0.25(16.60a) + 0.25(12.20y)

=  4.15a + 3.05y

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