Commutative Property of Multiplication: Definition & Examples

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  • 0:01 Commutative Property…
  • 1:28 Formula
  • 2:22 Example 1
  • 3:00 Example 2
  • 4:08 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, we talk about the commutative property of multiplication. We will see how it works in action and what it means for you when you are solving multiplication problems.

Commutative Property Definition

In this video lesson, we will talk about the commutative property of multiplication. This property tells us that it doesn't matter in what order you multiply numbers.

A good way to remember this is to think of the word commutative. What's another word that is similar? Commute is similar. When I think of commute, I think of commuting to work. Now, if on my way to work, one of the roads I normally take is blocked off due to construction, I would have to take a detour, a different way to get to work. But, even if I take a different route, I still end up in the same location - at work. It's the same with the commutative property of multiplication; you might have to multiply numbers in a different order to make the problem easier to solve, but your end result - your answer - will still be the same.

For example, multiplying 3 * 2 will give you the same answer as multiplying 2 * 3. You can test it out visually too by picturing some oranges. For 3 * 2 you would have three rows of two oranges each. For the 2 * 3 you would have two rows of three oranges each.

Oranges arranged two different ways


In math, we have a formula that says the same thing. It is a * b = b * a. The different letters stand for different numbers. Notice how on the left side of the equal sign, we have a * b, and on the right side of the equal sign, the b comes first. So, this formula is also telling us that it doesn't matter in what order we multiply our numbers. We will still get the same answer.

Even though this formula only shows two numbers, the commutative property of multiplication also applies when you multiply more than two numbers. When we have more than two numbers, we can switch around the numbers any which way we want. For example, if we have 3 * 11 * 2, we can switch it around to 3 * 2 * 11 or 11 * 3 * 2. We will end up with the same answer either way.

Example 1

Let's look at an example. Compare 1 * 4 and 4 * 1. According to the commutative property of multiplication, both of these multiplication problems will give us the same answer. We can visualize the problem using anything we want. We can use boxes of French fries. Yum!

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