# DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION

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

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

More clearly,

## Distributive property of multiplication over addition - Examples

Example 1 :

Evaluate using distributive property : 7(10 + 2)

Solution :

7(10 + 2)  =  7(10) + 7(2)

7(10 + 2)  =  70 + 14

7(10 + 2)  =  84

Example 2 :

Evaluate using distributive property : 6(x + y)

Solution :

6(x + y)  =  6x + 6y

Example 3 :

Evaluate using distributive property : m(n + p)

Solution :

m(n + p)  =  mn + mp

Example 4 :

Evaluate using distributive property : 5(x² + y² + z²)

Solution :

5(x² + y² + z²)  =  5x² + 5y² + 5z²

Example 5 :

Evaluate using distributive property : m(m² + m + 5)

Solution :

m(m² + m + 5)  =  m.m² + m.m + 5m

m(m² + m + 5)  =  m³m² + 5m

## Distributive property of multiplication over addition - Word problems

Problem 1 :

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,

The sum of two different numbers  =  x + y

3 times the sum of two different numbers  =  3(x + y)

Problem 2 :

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

Solution :

Let "x" be the required number.

According to the question, we have

4(x + 5)  =  32

4x + 20  =  32

4x  =  12

x  =  3

Hence the required number is 3.

Problem 3 :

Write the given verbal phrase into algebraic expression

"6 times the sum of three different numbers"

Solution :

Let "x" ,"y" and "z" be the two different numbers.

Then,

The sum of three different numbers  =  x + y + z

6 times the sum of three different numbers  =  6(x + y + z)

Problem 4 :

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

Solution :

Let "x" be the required number.

According to the question, we have

7(3x + 6)  =  147

21x + 42  =  147

21x  =  105

x  =  5

Hence the required number is 5.

Problem 5 :

If 9 times the sum of 7 and 4 times of a number is 135, find the number.

Solution :

Let "x" be the required number.

According to the question, we have

9(7 + 4x)  =  135

63 + 36x  =  135

36x  =  72

x  =  2

Hence the required number is 2.

After having gone through the stuff given above, we hope that the students would have understood "Distributive property of multiplication over addition".

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