Commutative Property Practice Problems & Worksheets

Master the commutative property of addition and multiplication with step-by-step practice problems. Learn to reorder addends and factors efficiently.

πŸ“šWhat You'll Practice with Commutative Property
  • Apply the commutative property formula a+b=b+a in algebraic expressions
  • Reorder addends to create convenient number combinations for mental math
  • Solve mixed number addition problems using commutative property shortcuts
  • Identify when commutative property applies to addition but not subtraction
  • Use commutative property to simplify complex fraction addition problems
  • Master both addition and multiplication commutative property applications

Understanding The Commutative Property of Addition

Complete explanation with examples

The commutative property of addition lets us change the position of addends (numbers being added together) that are being added together in an expression without changing the end result - no matter how many addends there are!
We can use the commutative property in simple expressions as well as algebraic expressions, and more!

Let's define the commutative property of addition as:
a+b=b+a a+b=b+a

and in an algebraic expression:
X+number=number+X X+number=number+X

A - The Commutative Property of Addition

Detailed explanation

Practice The Commutative Property of Addition

Test your knowledge with 14 quizzes

Solve:

\( -5+4+1-3 \)

Examples with solutions for The Commutative Property of Addition

Step-by-step solutions included
Exercise #1

5β‹…5β‹…5β‹…2β‹…2β‹…2=? 5\cdot5\cdot5\cdot2\cdot2\cdot2=?

Step-by-Step Solution

We use the substitution property and organize the exercise in the following order:

5Γ—2Γ—5Γ—2Γ—5Γ—2= 5\times2\times5\times2\times5\times2=

We place parentheses in the exercise:

(5Γ—2)Γ—(5Γ—2)Γ—(5Γ—2)= (5\times2)\times(5\times2)\times(5\times2)=

We solve from left to right:

10Γ—10Γ—10= 10\times10\times10=

(10Γ—10)Γ—10= (10\times10)\times10=

100Γ—10=1000 100\times10=1000

Answer:

1000

Video Solution
Exercise #2

βˆ’5+2= -5+2=

Step-by-Step Solution

If we draw a line that starts at negative five and ends at 5

We will go from the point negative five two steps forward (+2) we will arrive at the number negative 3.

Answer:

βˆ’3 -3

Video Solution
Exercise #3

10βˆ’5βˆ’2βˆ’3= 10-5-2-3=

Step-by-Step Solution

Given that the entire exercise is with subtraction, we solve the exercise from left to right:

10βˆ’5=5 10-5=5

5βˆ’2=3 5-2=3

3βˆ’3=0 3-3=0

Answer:

0 0

Video Solution
Exercise #4

4βˆ’2+2βˆ’4= 4-2+2-4=

Step-by-Step Solution

Given that we are referring to addition and subtraction exercises, we solve the exercise from left to right:

4βˆ’2=2 4-2=2

2+2=4 2+2=4

4βˆ’4=0 4-4=0

Answer:

0 0

Video Solution
Exercise #5

3βˆ’2+10βˆ’x= 3-2+10-x=

Step-by-Step Solution

We solve the exercise from left to right:

3βˆ’2=1 3-2=1

1+10=11 1+10=11

Now we obtain:

11βˆ’x 11-x

Answer:

11βˆ’x 11-x

Video Solution

Frequently Asked Questions

What is the commutative property of addition with examples?

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The commutative property of addition states that a+b=b+a, meaning you can change the order of addends without changing the sum. For example, 4+7=11 and 7+4=11 give the same result.

Does the commutative property work for subtraction and division?

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No, the commutative property only works for addition and multiplication. For subtraction, 8-3=5 but 3-8=-5, showing different results. The same applies to division.

How do you use commutative property to make math easier?

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You can reorder numbers to create convenient combinations. For example, in 7+3+6+4, reorder to (7+3)+(6+4)=10+10=20, making mental math much simpler.

What grade level learns the commutative property?

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Students typically learn the commutative property in elementary school around 2nd-3rd grade for basic addition, then apply it to more complex problems including fractions and algebraic expressions in middle school.

Can you use commutative property with mixed numbers and fractions?

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Yes! You can reorder mixed numbers and fractions with common denominators. For example, 4β…”+3β…“+2²⁄₇+1³⁄₇ can be reordered to group fractions with the same denominators together for easier calculation.

What's the difference between commutative and associative properties?

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Commutative property changes the ORDER of numbers (a+b=b+a), while associative property changes the GROUPING with parentheses ((a+b)+c=a+(b+c)). Both help simplify calculations but work differently.

How does commutative property work in algebraic expressions?

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In algebra, you can write X+7=7+X where X represents any number. When X=4, both 4+7 and 7+4 equal 11, proving the property works with variables too.

What are common mistakes students make with commutative property?

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The biggest mistake is trying to apply it to subtraction or division. Students also sometimes confuse it with associative property or forget that it only changes order, not the actual numbers being used.

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