*Trisha Fyfe*Show bio

Trisha has taught college and K-12 English, reading, writing, and math. She has a master's degree in teaching.

Lesson Transcript

Instructor:
*Trisha Fyfe*
Show bio

Trisha has taught college and K-12 English, reading, writing, and math. She has a master's degree in teaching.

The commutative property of addition states that when adding numbers together the result will stay the same no matter the order. Practice this through addition problems, and see how it also holds true for multiplication as well.
Updated: 12/20/2021

You take two books to school in your backpack. When you get there, your teacher decides that your backpack isn't heavy enough, and she gives you three more books to take home. How many books are in your backpack now? Let's add these up. 2 + 3 = 5. You have five books to take home.

But what if you started off with three books, and then your teacher gave you two more books? Does the number of books in your backpack change when we switch the order around? 3 + 2 = 5.

Nope. Sorry, but you're still going home with five books.

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Why was the answer still five even though the numbers were switched around?

This is an example of the **commutative property of addition**, which says that you can add numbers in any order and the answer will always be the same. Let's take a deeper look.

In our example about books, we showed you two different ways you can end up with five books in your backpack. As you saw, the two and the three switched places, but the answer stayed the same.

Let's practice with this a bit more. After carrying all those heavy books, you're hungry! Fruit sounds pretty good right now, and you have two choices. You can eat two bananas first and then one apple. Or you can eat one apple first and then two bananas. Will one choice give you more snacks than the other?

Let's figure this out.

2 + 1 = 3

or

1 + 2 = 3

The answers are exactly the same again, which means the number of snacks is the same. So, no matter how you add these numbers together, the answer remains the same.

Okay, you got this. Let's go one step further. You can also use this property in multiplication. Let's say you are getting ready to plant two gardens. How many seeds will you need? In one garden, you will have three rows of eight plants.

3 x 8 = 24 seeds

In your other garden, you will have eight rows of three plants.

8 x 3 = 24 seeds

Did you notice that the number of seeds is the same for each garden? The **commutative property of multiplication** says that you can multiply numbers in any order and the answer will always be the same.

Even though your gardens look different (one is longer and one is taller) the number of seeds is exactly the same! It doesn't matter whether you multiply 3 x 8 or 8 x 3. You get 24 both times.

Let's practice a bit more. How much money do you have for seeds? You pull some dollar bills out and sort them into piles on the table. First, you put down six piles of two dollars. Just in case, you count again. This time you put down two piles of six dollars.

Now the important question: how many dollars do you have?

Let's figure this out.

6 x 2 = 12

or

2 x 6 = 12

The answers are exactly the same again, which means the amount of money is the same. The order in which you multiply these numbers doesn't matter because of the commutative property.

In review, the **commutative property** in math tells us that we can add or multiply numbers in any order and the answer will be the same each and every time! This is just one of the reasons why we see the same answers in totally different math problems.

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