# Distributive Property of Addition || Definition, example and problems

## What is Distributive Property of Addition?

Distribution means “expansion” in English

The property says that the multiplication of sum of numbers is equal to sum of multiplication of individual numbers.

The property basically expand the multiplication operation on the sum of numbers.

According to distributive property

Where A, B & C can be any possible number.

In the above expression, you can observe that the parenthesis is replaced by multiplication of outside number A.

### Distributive Property of Addition Example

Let us understand the concept with some examples:

Example 01
Let A = 10, B = 5, C = 3

Calculating A ( B + C )
⟹ 10 ( 5 + 3 )
⟹ 10 x 8
⟹ 80

Now calculate, A.B + A.C
⟹ (10. 5) + (10 . 3)
⟹ 50 + 30
⟹ 80

Hence, A (B + C ) = A.B + A.C
So, The distributive property is verified

Example 02
Arrange the algebraic expression using distributive property
⟹ 6 (x + y)

The algebraic expression can be written as:
⟹ 6.x + 6.y

Example 03
Rearrange the expression using distributive property of addition
⟹ 5x + 10

Solution
The expression can be written as:
⟹ 5.x + 5.2

Taking number 5 as common and applying distributive property
⟹ 5 (x + 2)

### How to expand or reduce algebraic expression using Distributive Property

You will be using this property while solving algebra problems, so its important to know the method of application in different problems.

Reducing the expression
If the given expression has common element, you can reduce it easily through distributive property.

Example 01
7x + 14

The expression can be arranged as:
⟹ 7.x + 7.2

Here number 7 is the common element, so take it out & apply distribution property
⟹ 7 ( x + 2 )

This is the reduced algebraic expression

Example 02
Expand the expression using Distributive property
5 ( x + 3 )

Remove the parenthesis and apply distributive property
⟹ 5.x + 5.3
⟹ 5x + 15

## Frequently asked Question – Distributive Property

### (01) How distributive property different from commutative property?

Commutative property say that movement of number in addition will have no effect of addition result

A + B = B + A

While distributive property is all about simplification of number multiplied with addition sum.
A ( B + C ) = A.B + A.C

### (02) Can we apply distributive property to subtraction of numbers?

YES!!
The distributive property is applicable for number multiplied to subtraction of number.

The distributive property of subtraction is provided with following expression.

### (03) How is distributive property different from associative property?

Associative property says that forming different groups in addition will not change the end result.
According to associative property of addition
(A + B) + C = A + (B + C)

While distributive property is all about simplifying the multiplication of number with pair of addition
A (B + C) = A.B + A.C

### (04) Does distributive property works in division?

Yes!!
Distributive property of division is very helpful to solve complex division problems in simple manner.

According to distributive property of division
(A + B ) / C = A/C + B/C

Example
Divide 108 by 9

108 can be written as 99 + 9

So the division can be expressed as:
⟹ (99 + 9) / 9

Using distributive property of division
⟹ 99/9 + 9/9
⟹ 11 + 1
⟹ 12

Note: The distributive property for division does not work for expression: A / (B + C)

## Problems on Distributive Property of Addition

(01) Solve the expression using distributive property
5 (a + b) – 2a

(i) 6a + 2b
(ii) 3a + 5b
(iii) 6a + 7b

⟹ 5 (a + b) – 2a

Using distributive property
⟹ 5a + 5b – 2a

Rearranging the numbers using commutative property
5a – 2a + 5b

3a + 5b

Option (ii) is the right answer

(02) Expand the expression using distributive property and find answer
7 ( 6 + 3)

(a) 63
(b) 69
(c) 71

Solution
⟹ 7 ( 6 + 3 )

Expanding the expression, we get;
⟹ 7.6 + 7.3
⟹ 42 + 21
⟹ 63

Option (a) is the right answer

(03) Does distributive property works in division of addition of numbers

(a) Yes
(b) No

Yes, Distributive property works in division of numbers.

The distributive property of division is given as:
( A + B ) / C = A/C + B/C

(04) Solve the below expression and select the right answer
2x ( 7y – 3 )

(a) 7x – 3y
(b) 21xy – 3x
(c) 14xy – 6x
(d) 7xy – 7x

Below is the given expression
⟹ 2x ( 7y – 3 )

Expanding the expression using distributive property
⟹ 2x . 7y – 2x . 3
⟹14xy – 6x

Option (c) is the right answer

(05) Reduce the below expression using distributive property
10x – 100

(a) 5 (x – 2)
(b) 10 (x – 10)
(c) 10 (x – 2)

Solution
Below is the given expression
10x – 100

The expression can be rewritten as:
10x – 10.10

Here number 10 is the common element on the above two expressions.
Taking the common element out..

10 (x – 10)

option (b) is the right answer

(06) Which of the following is correct statement for distributive property of division

(a) ( 6 + 5 ) / 2 = (6 / 2) + (5 / 2)
(b) 2 / (6 + 5) = (2 / 6) + (2 / 5)