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. 

Detailed Answer Key

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. 

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

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

WORD PROBLEMS

HCF and LCM  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 fractions

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