# DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER SUBTRACTION

Distributive property of multiplication over subtraction is a very useful property that lets us simplify expressions in which we are multiplying a number by the difference of two other numbers.

The property states that the product of a number and the difference of two other numbers is equal to the difference of the products.

More clearly,

## Practice Questions

Question 1 :

Evaluate using distributive property :

7(10 - 2)

Use distributive property.

7(10 - 2)  =  7(10) - 7(2)

7(10 - 2)  =  70 - 14

7(10 - 2)  =  56

Question 2 :

Evaluate using distributive property :

6(x - y)

Use distributive property.

6(x - y)  =  6x - 6y

Question 3 :

Evaluate using distributive property :

m(n - p)

Use distributive property.

m(n - p)  =  mn - mp

Question 4 :

Evaluate using distributive property :

5(x2 - y2)

Use distributive property.

5(x2 - y2)  =  5x2 - 5y2

Question 5 :

Evaluate using distributive property :

m(m2 - m)

Use distributive property.

m(m2 - m)  =  m ⋅ m2 - m ⋅ m

m(m2 - m)  =  m3 - m2

Question 6 :

Write the given verbal phrase into algebraic expression

"3 times the difference of two different numbers"

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

Question 7 :

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

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.

Question 8 :

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

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.

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

If you have any feedback about our math content, please mail us :

v4formath@gmail.com

We always appreciate your feedback.

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

Word problems on quadratic 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