Commutative Property of Multiplication

Contributor: Ashley Nail. Lesson ID: 13052

Wow! That's a lot of big words, but the commutative property is actually really easy! You switch two numbers around, and the answer stays the same! Learn to use this property while multiplying.


Operations and Algebraic Thinking, Rules and Properties

learning style
Kinesthetic, Visual
personality style
Lion, Otter
Grade Level
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

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Imagine you and your best friend sit down to lunch. On the table, you have 2 plates of cookies in front of you. Your friend has 6 plates of cookies. No fair!

  • Is there any way that you and your friend could have the same amount of cookies?

girls eating cookies

There is a way!

You can prove it through the commutative property of multiplication!

But first, let's back up and look at your and your friend's plates of cookies. You have 2 plates of cookies. On each plate, there are 6 cookies.

2 circles with 6 dots each

  • How would you figure out how many cookies you have?

You could add 6 + 6 and get 12. Or you could multiply 2 x 6 and get 12. 2 plates times 6 cookies each equals 12 cookies for you.

Now, let's look at your friend's plates of cookies. She has 6 plates. On each plate, there are 2 cookies.

6 circles with 2 dots each

  • How many cookies does your friend have?

12! The same as you! You figured that out by adding 2+ 2 + 2 + 2 + 2 + 2 or by multiplying 6 x 2.

Let's compare the two multiplication equations, or number sentences, you used.

  • 2 x 6 = 12
  • 6 x 2 = 12
  • What do you notice?

There are some similarities. They both have a 12. That is called the product. The product is the answer when you multiply.

They both have a 6 and a 2. Those are called factors. Factors are the numbers you multiply to get the product.

factors and products

This is the commutative property. The factors (6 and 2) are in different places, but the product (12) stays the same.

So you and your friend both have 12 cookies, even though you have a different number of plates in front of you. You have 2 plates and your friend has 6 plates.

empty plate

Now, continue to the Got It? section to go to the kitchen and practice the commutative property on your own!

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