# 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.

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

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

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6