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 13 quizzes

\( 11\times3+7= \)

Examples with solutions for The Commutative Property of Addition

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 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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