Commutative Property: Definition & Examples

Instructor: Joseph Vigil
In this lesson, you'll learn what the commutative property of addition and multiplication is, and you'll review a few situations that show this property in action. Then, you can test your knowledge in a brief quiz.

Counting Cupcakes

Mrs. Jimenez and Mrs. Garcia are baking cupcakes for their students' bake sale. The morning of the sale, Mrs. Jimenez brought 4 dozen cupcakes. Thirty minutes later, Mrs. Garcia brought 3 dozen cupcakes.

The cupcakes from both women add up to 7 dozen.
chart showing total cupcakes

As you can see from the chart, the women brought a total of 7 dozen cupcakes to the bake sale.

If we were to write an addition sentence from this chart, we would write:

4 + 3 = 7

But what if Mrs. Garcia had brought her 3 dozen cupcakes first, and Mrs. Jimenez brought her 4 dozen thirty minutes later? Our chart would look like this:

Still a total of 7 dozen cupcakes.
chart showing total cupcakes

Mrs. Garcia's cupcakes come first now, but we still have a total of 7 dozen cupcakes. The order in which the women brought their cupcakes didn't change the total number of cupcakes. We can also see this in the addition sentence based on the chart:

3 + 4 = 7

The order doesn't affect the sum because when we're adding, all we're doing is bringing objects together into one group. So no matter what order they come in, they're all put into the same group.

So the commutative property of addition states that you can add numbers in any order and you'll still get the same sum.

The commutative property of addition even works with more than two numbers.

Pitching In

Let's say, for example, Charles, his sister, Patty, and his brother, Franklin, chip in to buy their mother a TV for her birthday. Charles put in $500, then Patty put in $300, and Franklin put in $200. We can make a chart showing their contributions.

All the contributions add up to 1,000 dollars.
chart showing total contributions

We can see from the chart that the total amount of money is $1,000. If we were to write the corresponding addition sentence, it would be:

500 + 300 + 200 = 1,000

But what if Franklin gave his money first, followed by Patty, and Charles gave his money last? Now our chart would look like this:

Still a total of 1,000 dollars.
chart showing total contributions

And our new addition sentence would look like this:

200 + 300 + 500 = 1,000

Again, the order of the numbers we're adding doesn't change the sum. The commutative property of addition holds true no matter how many numbers you add together.

After School Tutoring

Mr. Olson has a tutoring group that he works with after school. It consists of 6 students.

To accommodate those students, he can arrange his desks this way:

This arrangement yields a total of 6 desks.
chart showing total number of desks

Here, we have 2 rows of 3 desks for a total of 6 desks. We could write a multiplication sentence from this chart:

2 * 3 = 6

Mr. Olson could also arrange his desks this way:

New arrangement with the same numbers, still 6 desks.
chart showing total number of desks

Now, he has 3 rows of 2 desks. Even though he's changed the desks' arrangement, he still has the same total of 6 desks. We can also see this in the new multiplication sentence based on this chart:

3 * 2 = 6

When multiplying, the order doesn't affect the product because all we're doing is describing the same quantity in a different way.

So the commutative property of multiplication states that you can multiply numbers in any order and you'll still get the same product.

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

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 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 risk-free for 30 days!
Create an account
Support