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Commutative Property of Addition: Definition & Example

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Instructor: Karin Gonzalez

Karin has taught middle and high school Health and has a master's degree in social work.

The commutative property of addition states that the sum of any two addends is the same regardless of order. Explore this definition of the commutative property with numerical and real-life examples, along with the application of algebraic expressions. Updated: 10/22/2021

The Commutative Property of Addition

First of all, addition is the process of adding something to something else. In math, it is the process of adding two or more numbers or amounts together. We call the resulting number a sum.

The commutative property of addition, also called the order property of addition, states that when two numbers are added, the sum is the same even if you switch the order of the numbers being added. Those two numbers being added are called addends. Let's look at a simple example:

2 + 4 = 4 + 2

Even if we switch the order of the addends (2 and 4), we still get 6, so 2 plus 4 equals 4 plus 2!

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  • 0:00 The Commutative…
  • 0:40 Using the Property in…
  • 1:16 Other Examples
  • 2:04 Application of…
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Using the Property in Real Life

Imagine that you had two jellybeans: a red one and a green one. It won't matter if you eat the green jellybean before the red one or the red one before the green one; the result is still that you ate two jellybeans. This is a real life example of the commutative property of addition at work!

But, sometimes the order of doing things does make a difference. For example, if you put on your socks after your shoes, you would look pretty silly and be quite uncomfortable, no? This is an example of a time where order does matter and makes a big difference on the outcome. So this would not be similar to how the commutative property of addition works.

Other Examples

In the first example in this lesson, two numbers were used to illustrate the commutative property of addition. You can use numerous numbers and the property will still work. It is just important that you are using the same numbers on each side!

Let's look at the following examples:

1 + 3 = 3 + 1

Here, we are saying that one plus three equals three plus one. Because we are working with solely numbers here, we can attest this statement as being true. Both sides of the equation give us 4, and it does not matter that the one and three were switched.

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