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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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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 addition and what it means when you are adding numbers together. Learn how it can help you solve addition problems faster.

We begin with the definition for the **commutative property of addition**. Simply put, it says that the numbers can be added in any order, and you will still get the same answer. For example, if you are adding one and two together, the commutative property of addition says that you will get the same answer whether you are adding 1 + 2 or 2 + 1.

This also works for more than two numbers. Say you are adding one, two and three together (1 + 2 + 3). The commutative property of addition says that you can also add 2 + 1 + 3 or 3 + 2 + 1 and still get the same answer.

Let's think about marbles for a minute. Let's say we have two groups of marbles. One group only has one marble and the other group has two marbles. How many marbles do we have all together? We have three. Now, does it matter where you place your groups of marbles? For example, how many marbles will you have if you have one marble at the top of the stairs and two marbles at the bottom of the stairs? We still have three; we just have to climb the stairs to get all the marbles.

Now, what if you switched the two groups, so that you have two marbles at the top of the stairs and one marble at the bottom of the stairs? How many total marbles will you have? You still have three. It doesn't matter where you place your groups of items, you will still have the same total. This is what the commutative property of addition is all about.

In math, you know how we have formulas for everything. We also have a formula for the commutative property of addition. Formulas help us to generalize our problems. They use letters in place of numbers to let us know that the formula applies to all numbers. So, the formula for the commutative property of addition is *a* + *b* = *b* + *a*. See how the orders of our letters are switched around on opposite sides of the equals sign? This tells us that it doesn't matter what order we add our numbers in; the total will still be the same.

Let's look at some examples of the commutative property of addition in action: 4 + 6. Let's see if the commutative property of addition works for this problem. What is 4 + 6? You can picture two groups of puppies if it will help. One group has four puppies and the other group has six puppies. How many puppies do we have in total? We have ten.

What about 6 + 4? What does that equal? We can still use our puppies to help us visualize the problem, but we will swap the locations of our groups of puppies. How many puppies do we have now? We still have ten. After all, we didn't add or take away any puppies so we would expect our total to be the same.

Let's look at one more problem: 3 + 1 + 7. For this problem, we can actually use the commutative property of addition to help us solve the problem faster. If we are familiar with what numbers add up to ten, we will see right away that 3 + 7 = 10.

We can use the commutative property of addition to rearrange the problem so that it looks like this: 3 + 7 + 1. Now we can first add the 3 + 7. We get 10. What is 1 more than 10? 11.

Does this equal our original problem? We can again visualize the problem by picturing three groups of something. How about three groups of toy cars? We have three cars in our first group, one car in our second group and seven cars in our third group. How many total cars do we have? Counting them all, we have 11, the same as when we changed the order of the problem. The commutative property of addition works!

Let's review what we've learned now. We learned that the **commutative property of addition** tells us numbers can be added in any order and you will still get the same answer. The formula for this property is *a* + *b* = *b* + *a*. For example, adding 1 + 2 or 2 + 1 will give us the same answer according to the commutative property of addition.

After you've reviewed this video lesson, you should be able to:

- Define the commutative property of addition
- Identify the formula for this property

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- Commutative Property of Addition: Definition & Examples 5:02
- The Multiplication Property of Zero: Definition & Examples 2:40
- Distributive Property: Definition, Use & Examples 6:20
- Reflexive Property of Equality: Definition & Examples 3:43
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- Multiplication Property of Equality: Definition & Example 4:05
- Division Property of Equality: Definition & Example 3:51
- Transitive Property of Equality: Definition & Example 3:39
- Symmetric Property of Equality: Definition & Examples 3:26
- Go to 6th-8th Grade Math: Properties of Numbers

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