What is the Commutative Property of Addition?

The commutative property of addition tells us that we can add things in any order and still get the same sum. The commutative property is one of the building blocks for the rules of algebra. Here's an example of the property in use:
2 + 4 = 4 + 2

The commutative property of addition also applies to variables in the same way it applies to numbers. Here's an example:
a + b = b + a

When to use it: The Commutative Property is Everywhere

This math property is simple and still very useful. When we are re-arranging equations and performing algebraic maneuvers, the commutative property of addition allows us to write summed numbers and variables in any order. You may not even notice when you use it, but any time you rearrange summed terms on one side of an equation, you are using the commutative property of addition!

In math, something is commutative if changing the order of numbers does not affect the result. The commutative property also applies to multiplication. Called the commutative property of multiplication, it tells us that numbers and variables can be multiplied in any order while having the same result.

Commutative Property Example Problems

Let's do a couple of example problems together to reinforce our understanding of the commutative property of addition.

Example Problem 1

Prove the commutative property of addition by calculating the sum of 5 and 8.

Solution:

1. Let's write out the equation for summing 5 and 8 with the numbers in both possible orders.
2. 5 + 8 = 13
3. 8 + 5 = 13
4. Therefore, 5 + 8 = 8 + 5.

Example Problem 2

Following the rules of algebra, rewrite the equation 3b + 4c + a = 9 so the variables are in alphabetical order.

Solution:

1. The commutative property of addition tells us that we can add things in any order and still get the same sum.
2. Let's change the order of terms on the left-hand side of this equation.
3. This results in: a + 3b + 4c = 9