# Commutative Property of Addition: Definition & Examples

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• 0:02 Definition
• 1:52 Formula
• 2:33 Example 1
• 3:23 Example 2
• 4:29 Lesson Summary

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Instructor: Yuanxin (Amy) Yang Alcocer

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

## Commutative Property of Addition: Definition

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.

## Formula

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.

## Example 1

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.

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