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Commutative Property of Multiplication: Definition and Example | EDU.COM - AI智能索引
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Commutative Property of Multiplication: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Commutative Property of MultiplicationCommutative Property of Multiplication: Definition and ExampleTable of ContentsDefinition of Commutative Property of Multiplication

The commutative property of multiplication states that changing the order of factors in multiplication does not affect the product. The word "commutative" comes from "commute," which means to move around or travel. This property allows us to reorder numbers when multiplying them without changing the result. For example, 5×35 \times 35×3 equals 3×53 \times 53×5, with both expressions yielding 151515.

Multiplication itself is essentially repeated addition, allowing us to simplify calculations. The commutative property applies specifically to addition and multiplication operations but not to subtraction or division. This important distinction helps us understand which mathematical operations allow factors to be rearranged freely. For instance, while 4×7=7×4=284 \times 7 = 7 \times 4 = 284×7=7×4=28, division such as 8÷2=48 ÷ 2 = 48÷2=4 is not the same as 2÷8=0.252 ÷ 8 = 0.252÷8=0.25.

Examples of Commutative Property of Multiplication Example 1: Visual Representation with Brick Arrangements Problem:

Show that 4×34 \times 34×3 equals 3×43 \times 43×4 using a physical model.

Step-by-step solution:

Step 1, Let's understand what 4×34 \times 34×3 represents:

444 rows with 333 bricks in each row.

Step 2, Count the total number of bricks:

Total bricks === Number of rows × Number of bricks in each row Total bricks =4×3=12= 4 \times 3 = 12=4×3=12

Step 3, Let's rearrange our bricks to represent 3×43 \times 43×4:

333 rows with 444 bricks in each row.

Step 4, Count the total bricks again:

Total bricks === Number of rows ××× Number of bricks in each row Total bricks =3×4=12= 3 \times 4 = 12=3×4=12

Step 5, Notice that despite changing the arrangement (the order of multiplication), the total number of bricks remains the same: 121212. This demonstrates the commutative property of multiplication.

Example 2: Real-Life Application with Cost Calculation Problem:

Robin wants to buy 333 bars of chocolate. Each bar costs $10\$10$10. How much money does Robin need?

Step-by-step solution:

Step 1, Identify what we're calculating: the total cost of multiple identical items.

Method 1: We can calculate this as (Number of chocolates) ××× (Cost of each chocolate). Total cost =3×$10=$30= 3 \times \$10 = \$30=3×$10=$30 Method 2: We can also calculate this as (Cost of each chocolate) ××× (Number of chocolates). Total cost =$10×3=$30= \$10 \times 3 = \$30=$10×3=$30

Step 2, Notice that we get the same answer both ways. This real-world example shows that the order of multiplication doesn't change the final result.

Step 3, Remember this property makes calculations easier, especially when working with larger numbers or mental math.

Example 3: Fill in the Blanks Using the Commutative Property Problem:

Complete the following equations using the commutative property:

4×5=5×____4 \times 5 = 5 \times \_\_\_\_4×5=5×____ 3×___=6×33 \times \_\_\_ = 6 \times 33×___=6×3 16×2×4=2×____×416 \times 2 \times 4 = 2 \times \_\_\_\_ \times 416×2×4=2×____×4 Step-by-step solution:

Step 1, For equation 1:

Since the commutative property states that order doesn't matter in multiplication, if 4×5=204 \times 5 = 204×5=20, then 5×45 \times 45×4 must also equal 202020. Therefore, 4×5=5×44 \times 5 = 5 \times 44×5=5×4

Step 2, For equation 2:

Look at the right side: 6×3=186 \times 3 = 186×3=18 For the left side to equal 181818, we need 3×6=183 \times 6 = 183×6=18 Therefore, 3×6=6×33 \times 6 = 6 \times 33×6=6×3

Step 3, For equation 3:

Using the commutative property, we can reorder the factors without changing the result If 16×2×4=12816 \times 2 \times 4 = 12816×2×4=128, then 2×16×42 \times 16 \times 42×16×4 must also equal 128128128. Therefore, 16×2×4=2×16×416 \times 2 \times 4 = 2 \times 16 \times 416×2×4=2×16×4

Step 4, Key insight: These examples show that you can reorder any set of multiplicands (numbers being multiplied) and still get the same product, which can make calculations much simpler.

Comments(6)CChefHenryNovember 4, 2025This page really helped! I've used the examples to explain the commutative property of multiplication to my students. It's a great resource.

MCMs. CarterSeptember 10, 2025I’ve used this page to explain the commutative property to my kids, and the examples really made it click for them! It’s simple but super effective for building math confidence.

NNatureLover87August 27, 2025I used this clear definition and examples to explain the commutative property of multiplication to my 3rd grader, and it really clicked for them! The visual examples were super helpful.

NNatureLover25August 20, 2025I’ve used this page to help my kids understand the commutative property of multiplication, and the examples made it so simple for them to grasp. Great resource for parents and teachers!

MMathMom25August 6, 2025I used this definition to explain multiplication to my 3rd grader, and it really clicked for her! The examples made it super easy to show how order doesn’t matter. Thanks!

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