Commutative Property

Last Updated on February 15, 2024.

The commutative property is stating that if we change the order of the terms in addition or multiplication, it will not change our outcome.

Online GED Classes

Get a GED Diploma quickly.
It doesn’t matter when you left school.

Easy Lessons | Practice Tests | Add-ons


You may remember this easily as “commute” means to travel or move.

1. Identify the commutative property from the choices below.

Question 1 of 2

2. Which is not commutative?

Question 2 of 2


This lesson is provided by Onsego GED Prep.

Next lesson: Associative Property
This lesson is a part of our GED Math Study Guide.

Video Transcription

There will be many times in algebra when we have to simplify expressions.

The properties of real numbers are providing tools to help us to simplify complicated expressions. Algebra’s commutative property is often used for the simplification of algebraic expressions.

The commutative property of addition is stating that when we add two numbers, we can change the order of those numbers without affecting their sum.

Online GED Classes – Fast and Easy

Prepare Quickly To Pass The GED Test.
Get Your Diploma in 2 Months.

Example: 30 + 25 has exactly the same sum as 25 + 30.

30 + 25 equals 55
25 + 30 equals 55

Multiplication is behaving in the same way.

The commutative property of multiplication states that when we multiply 2 (two) numbers, we are able to change their order and this will not affect the product. For example, 7 • 12 gives us the exact same product as will 12 • 7.

7 • 12 = 84
12 • 7 = 84

The Commutative Property of Addition:

For the real numbers, a and b counts: a + b equals b + a.

The Commutative Property of Multiplication:

For the real numbers, a and b counts: a • b equals b • a.

Please note that Subtraction is not commutative.

Example: 4 − 7 is not having the same difference as 7 − 4 has.
The − sign means subtraction here.
Just as subtraction doesn’t come commutative, neither does division.
Example: 4 ÷ 2 doesn’t have the same quotient as 2 ÷ 4.