Login
Copyright

Commutative Property: Definition & Review

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: How to Build and Reduce Fractions

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:00 Commutative
  • 0:35 Three Important Properties
  • 1:05 The Commutative Property
  • 3:20 Lesson Summary
Add to Add to Add to

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Login or Sign up

Timeline
Autoplay
Autoplay
Create an account to start this course today
Try it free for 5 days!
Create An Account

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Artem Cheprasov
In this lesson, you're going to learn the meaning of the commutative property as well as in which mathematical operations it is applicable and in which ones it is not.

Commutative

If you add a fourth of a bucket of water to a half bucket of water, you have three-fourths of a bucket of water. If instead you add half a bucket of water to a fourth of a bucket of water, how much do you have total? It's still just the same three-fourths of a bucket of water. It doesn't matter which bucket is added to which one; the total of both is always going to be the same. This is one example of something called the commutative property, where commutative is a word that describes something that is independent of order. Let's go over mathematical operations that are commutative and those that are not.

Three Important Properties

In general, I want you to know that there are three basic properties which describe how operations may work. The commutative property, which we'll get to shortly, the associative property, which deals with adding and multiplying numbers regardless of how they are grouped, and the distributive property, which deals with multiplying a single term with other terms inside a parentheses. These three properties are characteristics of some mathematical operations as opposed to rules. They describe how certain operations work but are not rules that state how all operations work.

The Commutative Property

With that out of the way, let's get to the important gist of the commutative property. Again, commutative means order doesn't matter. If you do an operation in one order, then do it in another order, you'll get the same answer. Remember that bucket example from the intro? It doesn't matter what order we pour the water in, from the first bucket to the second or vice versa the total amount will always be the same.

Also, like commuting to work, you take the same roads, it doesn't matter which direction you are driving. The distance you drive to work will be the same distance traveled, coming home from work. The order doesn't matter.

These are all metaphors for commutation. So why don't we get to some actual examples?

There are two main examples of operations that are commutative. They are addition and multiplication. In addition, it doesn't matter if you add 4 + 5 or 5 + 4 -- you still get 9. The order doesn't matter. The commutative property holds up even when there are more than two numbers. 1 + 2 + 3 = 2 + 3 + 1. As long as you are adding the same numbers, it doesn't matter what order you add them in, you'll get the same result. It boils down to this: a + b = b + a.

To unlock this lesson you must be a Study.com Member.
Create your account

Register for a free trial

Are you a student or a teacher?
I am a teacher
What is your educational goal?
 Back

Unlock Your Education

See for yourself why 10 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back

Earning College Credit

Did you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it free for 5 days!
Create An Account
Support