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Commutative Property of Addition: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Commutative Property of AdditionCommutative Property of Addition: Definition and ExampleTable of ContentsDefinition of Commutative Property of Addition

The commutative property of addition is a fundamental mathematical concept that states the order of addends does not affect the sum. When we add numbers, we can rearrange them in any order without changing the final result. Mathematically, this property is represented as a+b=b+aa + b = b + aa+b=b+a, where aaa and bbb can be whole numbers, integers, decimals, or fractions. This property makes addition more flexible and often simplifies calculations in arithmetic problems.

Not all mathematical operations follow the commutative property. While addition and multiplication both follow this property (a×b=b×aa \times b = b \times aa×b=b×a), subtraction and division do not. For subtraction, changing the order of numbers completely changes the result. For example, 4−3=14 - 3 = 14−3=1 but 3−4=−13 - 4 = -13−4=−1. Similarly, division also does not follow the commutative property. This distinction is important to understand when working with different arithmetic operations.

Examples of Commutative Property of Addition Example 1: Verifying the Commutative Property Problem:

Verify that "a+b=b+aa + b = b + aa+b=b+a", if a=33a = 33a=33 and b=30b = 30b=30.

Step-by-step solution:

Step 1, Let's examine the left side of the equation by substituting the given values:

a+b=33+30=63a + b = 33 + 30 = 63a+b=33+30=63

Step 2, Let's examine the right side of the equation:

b+a=30+33=63b + a = 30 + 33 = 63b+a=30+33=63

Step 3, Since both sides equal 63, we have verified that a+b=b+aa + b = b + aa+b=b+a when a=33a = 33a=33 and b=30b = 30b=30.

This confirms the commutative property of addition. Example 2: Using the Commutative Property to Fill in Blanks Problem:

Fill in the blanks: 20+_=_+20=5520 + \_ = \_ + 20 = 5520+_=_+20=55

Step-by-step solution:

Step 1, Recognize that this equation relies on the commutative property of addition, which means the missing number must be the same in both blanks.

Step 2, Let's call this missing number bbb and set up the equation:

20+b=5520 + b = 5520+b=55

Step 3, Solve for the unknown value:

b=55−20=35b = 55 - 20 = 35b=55−20=35

Step 4, We can fill in the blanks with our solution:

20+35=35+20=5520 + 35 = 35 + 20 = 5520+35=35+20=55 Example 3: Solving a Word Problem Using the Commutative Property Problem:

At the school fair, Maya collected 353535 tickets from the ring toss game and 181818 tickets from the basketball shoot game. How many tickets did Maya collect in total? Use the commutative property of addition to solve this problem in two different ways.

Step-by-step solution:

Step 1, Let's add the tickets in the order they were mentioned in the problem:

Maya has 353535 tickets from the ring toss game.

Maya has 181818 tickets from the basketball shoot game.

Adding these numbers: 35+18=5335 + 18 = 5335+18=53 tickets.

Step 2, Let's use the commutative property of addition. This property tells us that we can change the order of the numbers when adding, and we'll still get the same result.

So instead, we can add: 18+35=5318 + 35 = 5318+35=53 tickets.

Step 3, We can compare our two calculations:

35+18=5335 + 18 = 5335+18=53 tickets

18+35=5318 + 35 = 5318+35=53 tickets

Both ways give us the same answer!

Step 4, Maya collected 535353 tickets in total from both games.

Comments(7)AArtistDianaNovember 6, 2025This glossary page on the commutative property of addition is great! It helped my student grasp the concept easily. Thanks for the clear examples!

MMusicTutorIanNovember 5, 2025I've used this def to teach my students. It's super clear! The examples really helped them grasp the commutative property of addition.

NNatureLover85September 10, 2025I used the commutative property of addition examples from this page to help my kids with their homework—it made the concept so much easier for them to grasp. Great resource for parents and teachers!

NNatureLover25August 27, 2025I’ve used the commutative property of addition examples from this page to help my kids with homework. It’s such a simple concept, but the way it’s explained here really clicked for them!

MMomOf3AdventurersAugust 20, 2025I’ve used this page to explain the commutative property of addition to my students, and they loved the clear examples! It made the concept click for them. Great resource for parents and teachers!

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