Commutative Property of Multiplication Practice Problems

Master the commutative property of multiplication with step-by-step practice problems, examples, and exercises that help you understand how factor order doesn't change results.

πŸ“šPractice Commutative Property Skills You'll Master
  • Apply the commutative property to reorder multiplication factors for easier calculation
  • Solve mixed fraction multiplication problems using commutative property shortcuts
  • Identify when factor rearrangement simplifies complex multiplication expressions
  • Work with algebraic expressions using the commutative property rule
  • Practice multi-step problems combining parentheses and commutative property
  • Build confidence with decimal and fraction multiplication using factor reordering

Understanding The Commutative Property of Multiplication

Complete explanation with examples

The commutative property of multiplication tells us that changing the order of factors in an expression doesn't change the answer - even if there are more than two!
Like the commutative property of addition, the commutative property of multiplication helps us simplify basic expressions, algebraic expressions and more.


We can define the commutative property of multiplication as:
aΓ—b=bΓ—a a\times b=b\times a

And in algebraic expressions:
XΓ—number=numberΓ—XX\times number=number\times X

A - The Commutative Property of Multiplication

Detailed explanation

Practice The Commutative Property of Multiplication

Test your knowledge with 13 quizzes

\( 11\times3+7= \)

Examples with solutions for The Commutative Property of Multiplication

Step-by-step solutions included
Exercise #1

Solve:

2βˆ’3+1 2-3+1

Step-by-Step Solution

We use the substitution property and add parentheses for the addition operation:

(2+1)βˆ’3= (2+1)-3=

Now, we solve the exercise according to the order of operations:

2+1=3 2+1=3

3βˆ’3=0 3-3=0

Answer:

0

Video Solution
Exercise #2

Solve:

3βˆ’4+2+1 3-4+2+1

Step-by-Step Solution

We will use the substitution property to arrange the exercise a bit more comfortably, we will add parentheses to the addition operation:
(3+2+1)βˆ’4= (3+2+1)-4=
We first solve the addition, from left to right:
3+2=5 3+2=5

5+1=6 5+1=6
And finally, we subtract:

6βˆ’4=2 6-4=2

Answer:

2

Video Solution
Exercise #3

Solve:

βˆ’5+4+1βˆ’3 -5+4+1-3

Step-by-Step Solution

According to the order of operations, addition and subtraction are on the same level and, therefore, must be resolved from left to right.

However, in the exercise we can use the substitution property to make solving simpler.

-5+4+1-3

4+1-5-3

5-5-3

0-3

-3

Answer:

βˆ’3 -3

Video Solution
Exercise #4

7+4+3+6=? 7+4+3+6=\text{?}

Step-by-Step Solution

To make solving the exercise easier, we try to add numbers that give us a result of 10.

Let's keep in mind that:

7+3=10 7+3=10

6+4=10 6+4=10

Hence we obtain a more manageable exercise to solve:

10+10=20 10+10=20

Answer:

20

Video Solution
Exercise #5

19+34+21+10+6=? 19+34+21+10+6=\text{?}

Step-by-Step Solution

In order to simplify our calculations, we try to add numbers that give us a round result.

Keep in mind that:

19+21=40 19+21=40

34+6=40 34+6=40

Now, we get a more manageable exercise to solve:

40+40+10=80+10=90 40+40+10=80+10=90

Answer:

90

Video Solution

Frequently Asked Questions

What is the commutative property of multiplication with examples?

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The commutative property of multiplication states that a Γ— b = b Γ— a, meaning the order of factors doesn't change the result. For example, 3 Γ— 5 = 15 and 5 Γ— 3 = 15. This property works with any numbers, including fractions, decimals, and algebraic expressions like X Γ— 2 = 2 Γ— X.

How do you use the commutative property to make multiplication easier?

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You can rearrange factors to create simpler calculations. For instance, instead of solving 7 Γ— 13 Γ— 6 Γ— 5 in order, rearrange it to (7 Γ— 13) Γ— (6 Γ— 5) = 91 Γ— 30 = 2,730. This makes mental math much easier by grouping numbers that multiply to round numbers.

Does the commutative property work for division?

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No, the commutative property does not work for division. For example, 12 Γ· 3 = 4, but 3 Γ· 12 = 0.25. Division is not commutative because changing the order of numbers changes the result.

What are some real world examples of commutative property in multiplication?

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Real-world examples include: calculating area (5 feet Γ— 3 feet = 3 feet Γ— 5 feet = 15 square feet), counting items in groups (4 boxes Γ— 6 items = 6 items Γ— 4 boxes = 24 total items), and calculating costs (3 items Γ— $7 each = $7 Γ— 3 items = $21 total).

How is the commutative property different from associative property?

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The commutative property changes the order of factors (a Γ— b = b Γ— a), while the associative property changes how factors are grouped: (a Γ— b) Γ— c = a Γ— (b Γ— c). Commutative focuses on rearranging, while associative focuses on regrouping without changing order.

What grade level learns the commutative property of multiplication?

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Students typically learn the commutative property of multiplication in 3rd grade as part of basic multiplication facts. However, they continue applying it through middle school and high school when working with algebraic expressions, fractions, and more complex calculations.

Can you use commutative property with more than two factors?

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Yes, the commutative property works with any number of factors. For example, in 2 Γ— 4 Γ— 7 Γ— 5, you can rearrange to 2 Γ— 5 Γ— 4 Γ— 7 = 10 Γ— 28 = 280. You can move any factors to any position to make calculation easier while keeping the same result.

How do you explain commutative property to struggling students?

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Use visual aids and real objects. Show that 3 groups of 4 objects equals 4 groups of 3 objects - both give 12 total items. Use arrays, pictures, or manipulatives to demonstrate that rearranging doesn't change the total quantity, just like rearranging factors doesn't change the multiplication result.

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