Back To Course

6th-8th Grade Math: Practice & Review55 chapters | 468 lessons

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

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

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
1 in chapter 3 of the course:

Back To Course

6th-8th Grade Math: Practice & Review55 chapters | 468 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
- Addition Property of Equality: Definition & Example 3:51
- Subtraction Property of Equality: Definition & Example 3:54
- 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

- Communications 104: Intro to Mass Communications I
- Art 104: History of Western Art II
- Inclusion in Recruitment, Interviews & Hiring
- Computer Science 105: Introduction to Operating Systems
- High School 101: High School Readiness
- History & Culture of Mass Communication
- Mass Communication & Modern Society
- Introduction to Mass Communication
- Mass Communication & Book Publishing
- Models & Theories of Mass Communication
- List of FTCE Tests
- CLEP Prep Product Comparison
- CLEP Exam vs. AP Test: Difficulty & Differences
- CLEP Tests for the Military
- How to Transfer CLEP Credits
- CLEP Exam Question Formats
- CLEP Exam Costs & Registration Deadlines

- Probability Density Function: Definition, Formula & Examples
- The Merchant in The Canterbury Tales: Character Analysis & Description
- A Christmas Carol Stave 1 Summary
- The Multiplier Effect in Economics: Definition, Formula & Example
- Wraparound Services for ELLs & Their Families
- Locating Information in a Factual Text
- Lasswell's Model of Mass Communication
- The Levels of the Memory Processing Model
- Quiz & Worksheet - Designing Information Systems
- Quiz & Worksheet - The Character of Macbeth
- Quiz & Worksheet - Importance of the Textile Industry
- Quiz & Worksheet - Persian Empire Gov't & Military
- Quiz & Worksheet - Drift Velocity & Mobility
- How to Cite Sources Flashcards
- Evaluating Sources for Research Flashcards

- Geometry Proofs: Help & Tutorials
- Holt United States History: Online Textbook Help
- SAT Subject Test US History: Practice and Study Guide
- Physics 101 Syllabus Resource & Lesson Plans
- Educational Psychology: Help and Review
- The History & Role of Political Parties
- Introduction to Organic Chemistry: Homework Help
- Quiz & Worksheet - Nicholaus Copernicus
- Quiz & Worksheet - Pathogens & Antibiotic Resistance
- Quiz & Worksheet - Formation of a Phosphodiester Bond
- Quiz & Worksheet - The Evolutionary History of Humans
- Quiz & Worksheet - Politics & Energy Resources

- Dinoflagellates: Characteristics, Examples & Classification
- Puerperal Fever: Definition & History
- Soil Activities for Kids
- Sunnyvale, CA Adult Education
- What is on the LSAT?
- AP Exam Registration Deadline
- Light for Kids: Activities & Experiments
- D-Day Lesson Plan
- Imperialism Lesson Plan
- Constitutional Convention Lesson Plan
- Sounds Experiments Lesson for Kids
- Story Elements Lesson Plan

Browse by subject