# Commutative Property of Addition You've Been Using Without Realizing

Addition possesses a commutative property, akin to but different from multiplication. Herein, you will find that property explained, with examples.

Omkar Phatak

Last Updated: Jan 7, 2019

*commutative property*.

About Addition

You might already be familiar with what is addition of two numbers, which is the most basic of operations in mathematics. Addition is summing up the value of two numbers, to get a bigger number.

Definition

To be able to understand the commutative property, you need to know what 'commutative' means. The exact meaning of commutative is an entity which is 'independent of order'. In this case, the commutative property of addition is stated as follows,

*the sum of two or numbers or variables is the same, irrespective of the order in which they are added*.

m + n = n + m

m + n = n + m

where n and m are variables. Thus, the gist of this property is that it doesn't matter in what order two or more variables are added. Even multiplication of two numbers is commutative in nature.

Examples

Here are some examples that will help you grasp the concept.

- a + b + c = c + b + a
- x + y = y + x
- 3 + 4+ 5 = 5 + 4+ 3 = 4 + 3 + 5 = 4 + 5 + 3
- 2+ 0 = 0 + 2
- 1 + 0 = 0 + 1
- a + 9 = 9 + a