DISTRIBUTIVE PROPERTY OF MULTIPLICATION

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

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

Distributive Property of Multiplication over Addition : 

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

Distributive Property of Multiplication over Subtraction : 

Practice Questions

Question 1 : 

Evaluate using distributive property :

7(10 + 2)

Answer :

Use distributive property.

7(10 + 2)  =  7(10) + 7(2)

7(10 + 2)  =  70 + 14 

7(10 + 2)  =  84

Question 2 : 

Evaluate using distributive property :

7(10 - 2)

Answer :

Use distributive property.

7(10 - 2)  =  7(10) - 7(2)

7(10 - 2)  =  70 - 14 

7(10 - 2)  =  56

Question 3 : 

Evaluate using distributive property :

6(x + y)

Answer :

Use distributive property.

6(x + y)  =  6x + 6y

Question 4 : 

Evaluate using distributive property :

m(n - p)

Answer :

Use distributive property.

m(n - p)  =  mn - mp

Question 5 : 

Evaluate using distributive property :

5(x² + y² + z²)

Answer :

Use distributive property.

5(x² + y² + z²)  =  5x² + 5y² + 5z²

Question 6 : 

Evaluate using distributive property :

m(m² - m)

Answer :

Use distributive property.

m(m² - m)  =  m ⋅ m² - m ⋅ m

m(m² - m)  =  m³ - m²

Question 7 : 

Write the given verbal phrase into algebraic expression

"3 times the sum of two different numbers"

Answer :

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

Question 8 : 

Write the given verbal phrase into algebraic expression

"7 times the difference of 5 times of a number and 4"

Answer :

Let x and y be the two different numbers.

Then, 7 times the difference of 5 times of a number and 4 is

=  7(7x - 5)

Use distributive property.

=  49x - 35

Question 9 : 

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

Answer :

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 10 : 

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

Answer :

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. 

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