# Commutative Property of Addition : Definition, Property & Example

## What is commutative property of addition?

Commutative means “ to move

The property says that even if we move around digits in the addition, the end result will be the same.

According to commutative property;

where a & b can be any possible number

### Commutative Property of Addition Example

Let us understand the concept with example:

Example 01
Let A = 5 & B = 6

Adding the two numbers
⟹ A + B
⟹ 5 + 6
⟹ 11

Changing the position of numbers
⟹ B + A
⟹ 6 + 5
⟹ 11

Hence, A + B = B + A
The commutative property is verified

Example 02
Let A = 32 and B = 10

⟹ A + B
⟹ 32 + 10
⟹ 42

Moving the numbers
⟹ B + A
⟹ 10 + 32
⟹ 42

Hence, A + B = B + A
Commutative property of addition is verified

Example 03
Solve the algebraic expression
2x – 7y + 9x

Using commutative property to move around digits
⟹ 2x + 9x – 7y
⟹ 11x – 7y

Example 04
Solve the equation
11x + 2y + 6x + 5y

Move the digits using commutative property
⟹ 11x + 6x + 2y + 5y
⟹ 17x + 8y

Example 05
Check if commutative property works in following expression
5 + 2 + 9

Solution
(a) Find the solution of above addition
5 + 2 + 9 = 16

(b) Changing the order of numbers
9 + 5 + 2 = 16

(c) Rearranging the numbers again
2 + 9 + 5 = 16

we can see that (a) = (b) = (c)
hence, the expression follows commutative property

## Frequently asked questions- Commutative Property of Addition

### How is commutative property of addition is different that associative property?

Commutative property allows movement of numbers in the expression while associative property allows formation of different groups in addition.

Commutative property
A + B = B + A

Associative Property
[A + B] + C = A + [B + C]

### Does the commutative property works in divisions also?

NO!!!
In Division, the commutative property does not work as changing the order of numbers will produce completely different results

### Can Commutative property applies in multiplication?

Yes!!
Commutative property works in multiplication as there is no change in result on changing the orders of the numbers.

Example
Let A = 4 and B = 6

⟹ A x B
⟹ 4 x 6
⟹ 24

Now changing the position of numbers
⟹ B x A
⟹ 6 x 4
⟹ 24

### How commutative property different from distributive property?

Distributive property is basically simplification of multiplication and addition operation.

According to distributive property:

In distributive property, the bracket is removed and replaced with multiplication operation with number outside the paranthesis.

While the Commutative Property simply tells that changing the order of number in addition does not affect the end result of addition

### Will Commutative Property works in subtraction operation?

NO!!

The property will not work as moving numbers in subtraction will yield completely different result

Example
Let A = 10 and B = 4

⟹ A – B
⟹ 10 – 4
⟹ 6

Now moving the number position
⟹ B – A
⟹ 4 – 10
⟹ – 6

Both the operation gives completely different results.

Hence commutative property does not work in subtraction

## Problems on commutative property of addition

(01) Which of the following example shows commutative property of addition

(a) 6 + 3 = 5 + 4
(b) 4 + 7 = 7 + 4
(c) 2 + 3 = 1 + 4

Option (b) is the right answer.
In option (b) digits are rotated to produce the same result which is the feature of commutative property of addition

(02) Find the value of x in the below expression which follow the rule of commutative property
23 + x = z
10 + y = z

(a) x = 13
(b) x = 20
(c) x = 10
(d) x = 30

Option (c) is the right answer

We know that in commutative property, same digits are rotated.

Observing the given expression;

hence,
y = 23 and x = 10

(03) Its given that x + y = 13; Find the value of y + x

(a) 13
(b) 10
(c) 17
(d) 15

Option (a) is the right answer.

The question involves straightforward use of commutative property.

(04) Solve the below expression using commutative property
9x + 7y + x + 5y

(a) 15x + 9y
(b) 11x + 8y
(c) 15x + 15y
(d) 10x+ 12y

Rearranging the expression using commutative property of addition

⟹ 9x + x + 7y + 5y

⟹ 10x + 12y

Option (d) is the right answer

(05) Can the below expression follow commutative property
x – y + z

(a) Yes
(b) No