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Quizzes > Mathematics

Commutative Property Practice Problems: 20-Question Quiz

Quick math quiz with instant feedback. Includes commutative addition practice.

Editorial: Review CompletedCreated By: Emma WaylandUpdated Aug 27, 2025
Difficulty: Moderate
Grade: Grade 4
Study OutcomesCheat Sheet
Colorful paper art promoting Commutative Swap Challenge math quiz for middle school students.

This quiz helps you practice the commutative property in addition and multiplication and notice when order does or does not change the answer. Work through 20 quick questions with instant feedback to build speed and accuracy. For more practice, try simplifying expressions practice, the evaluating expressions quiz, or warm up with a basic math quiz.

Which equation correctly shows the commutative property of addition?
4 + 7 = 4 - 7
4 + 7 = 7 + 4
4 x 7 = 7 x 4
4 - 7 = 7 - 4
The commutative property of addition states that the order of addends does not affect the sum. In this equation, swapping 4 and 7 still gives an equivalent expression.
Which equation correctly shows the commutative property of multiplication?
6 x 9 = 9 x 6
6 x 9 = 9 - 6
6 + 9 = 9 + 6
6 x 9 = 6 + 9
The commutative property for multiplication confirms that switching the order of the factors does not change the product. The equation 6 x 9 = 9 x 6 shown here correctly represents this property.
If 8 + 3 = 11, what is the result of swapping the numbers using the commutative property?
3 + 8 = 12
8 - 3 = 5
8 x 3 = 24
3 + 8 = 11
The commutative property of addition shows that the sum remains the same regardless of the order of the addends. Therefore, swapping 8 and 3 still results in 11.
Which statement best describes the commutative property of addition?
Changing the order of numbers reverses the sum
Changing the order of numbers does not change the sum
Changing the order of numbers results in a different operation
Changing the order of numbers significantly changes the sum
The commutative property of addition means that adding numbers in any order results in the same sum. This concept is fundamental to understanding how addition works.
Using the commutative property, which expression is equivalent to 12 + 5?
12 x 5
5 + 12
12 - 5
5 - 12
The commutative property allows us to swap the order of numbers in addition without affecting the result. Therefore, 12 + 5 is equivalent to 5 + 12.
Does the commutative property hold true for subtraction?
Only when the numbers are equal
Yes, subtraction is commutative
Only with positive numbers
No, changing the order in subtraction changes the result
Subtraction is not commutative because the order of the numbers matters. The result of subtracting in one order differs from the result when the order is reversed.
Does the commutative property apply to division?
Only for whole numbers
Only when the dividend and divisor are identical
No, division is not commutative
Yes, dividing in any order yields the same quotient
Division does not follow the commutative property, meaning that changing the order of the numbers typically results in a different value. Therefore, division does not work like addition or multiplication in this regard.
Which equation demonstrates the incorrect use of the commutative property?
5 + 9 = 9 + 5
4 + 6 = 6 + 4
3 x 8 = 8 x 3
7 - 2 = 2 - 7
The subtraction example is incorrect because subtraction does not have the commutative property. While addition and multiplication do, reversing the order in subtraction gives a different result.
If 0 is added to any number, what does the commutative property indicate about the result?
The result remains the same
It doubles the number
The result changes depending on order
It becomes zero
The identity property of addition states that adding zero to any number does not change its value. The commutative property supports this by allowing the number and zero to be interchanged without affecting the sum.
Consider the expressions: 4 x 5 and 5 x 4. Which property justifies their equality?
Distributive Property
Associative Property
Commutative Property
Identity Property
The equality of 4 x 5 and 5 x 4 is due to the commutative property of multiplication. This property states that switching the order of factors does not change the product.
Which of the following is a valid application of the commutative property?
3 x 2 x 1 = 1 x (2 x 3)
3 - 2 - 1 = 2 - 1 - 3
3 + 2 + 1 = 3 + (2 + 1)
3 + 2 + 1 = 1 + 2 + 3
Changing the order of the terms in an addition expression is a direct application of the commutative property. The first option correctly rearranges the addends while preserving the overall sum.
The commutative property is essential for simplifying which types of problems?
Problems involving division only
Problems involving exponentiation
Problems involving subtraction
Problems involving multiplication and addition
The commutative property applies directly to addition and multiplication. It allows you to rearrange terms to simplify calculations in these types of problems.
Which of the following is an example that does NOT follow the commutative property?
9 - 3 = 3 - 9
7 x 2 = 2 x 7
8 + 4 = 4 + 8
5 + 0 = 0 + 5
Subtraction is an operation that does not satisfy the commutative property. The expression 9 - 3 is not equal to 3 - 9, which makes it a clear exception.
In the expression a + b, if a = 10 and b = 15, what does the commutative property tell us?
10 + 15 equals 15 + 10
The order must be maintained for accuracy
10 + 15 is different from 15 + 10
Swapping the numbers results in a different value
According to the commutative property of addition, the order of addends does not affect the final sum. Thus, 10 + 15 is equal to 15 + 10.
For the multiplication expression b x c, which statement is true due to the commutative property?
It only applies when b equals c
It is only valid for positive numbers
Changing the order of factors changes the product
The product remains unchanged if the factors are swapped
The commutative property of multiplication assures that switching the order of factors does not alter the product. This holds true for all numbers, regardless of their values.
Identify which of the following expressions is equivalent to 2(x + y) + 3(y + x) by using the commutative property.
5(x - y)
2x + 3y
6x + 6y
5(x + y)
Recognizing that (x + y) is identical to (y + x) by the commutative property allows you to combine 2(x + y) and 3(x + y) into 5(x + y). This simplification confirms the proper application of the property.
Which of these equations requires both the commutative and associative properties to simplify correctly?
8 - (3 - 1) = (8 - 3) - 1
(2 x 3) = (3 x 2)
4 + (1 + 6) = 1 + (4 + 6)
3 + 5 = 5 + 3
The equation 4 + (1 + 6) = 1 + (4 + 6) requires reordering and regrouping the numbers to achieve the same result. This process uses both the commutative property (to swap numbers) and the associative property (to change grouping).
Which of the following adjustments cannot be justified by the commutative property?
Changing 7 + 2 to 2 + 7
Changing 9 - 4 to 4 - 9
Changing 5 + 0 to 0 + 5
Changing 8 x 3 to 3 x 8
The commutative property applies to addition and multiplication but not to subtraction. Hence, transforming 9 - 4 into 4 - 9 is not justified by this property.
In an algebraic expression, a + b + c, which of the following represents a valid rearrangement using the commutative property?
b - a + c
c + a + b
a - b + c
c - a - b
The commutative property allows you to rearrange the terms in an addition expression without changing the result. The choice 'c + a + b' is a valid rearrangement that preserves the original sum.
Consider the expressions (2 + 3) + 4 and 2 + (4 + 3). Which property (or properties) justify the equality of these expressions?
Neither property applies
Only the commutative property
Both the commutative and associative properties
Only the associative property
Reordering and regrouping numbers in the expressions require both the commutative property (to swap 3 and 4) and the associative property (to change the grouping). Together, these properties justify the equality of the two expressions.
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Study Outcomes

  1. Apply the commutative property to simplify arithmetic expressions.
  2. Identify equivalent forms of mathematical equations using number swaps.
  3. Demonstrate enhanced problem-solving skills in commutative property exercises.
  4. Analyze expressions to verify the accuracy of commutative transformations.
  5. Build confidence in tackling commutative property questions on tests and exams.

Commutative Property Practice Cheat Sheet

  1. Understand the Commutative Property of Addition - This playful property tells you that swapping addends doesn't change the sum, so 4 + 5 will always equal 5 + 4. It's like trading stickers with a friend - you'll still have the same total! Get hands‑on practice with real examples and boost your confidence.
  2. Learn the Commutative Property of Multiplication - Just like addition, you can flip the factors in a multiplication problem without altering the product, so 3 × 7 equals 7 × 3 every time. Imagine arranging groups of cookies in different orders - you'll still count the same total. This trick saves time and makes mental math a breeze.
  3. Recognize Non‑Commutative Operations - Beware: subtraction and division don't play by the same rules. Changing the order in 5 − 2 or 10 ÷ 2 will throw off your result - 5 − 2 is not the same as 2 − 5! Spotting these exceptions helps you avoid calculation pitfalls.
  4. Apply the Property to Algebraic Expressions - Variables behave just like numbers under commutativity, so a + b equals b + a and ab equals ba. This means you can rearrange terms to simplify expressions and solve equations faster. Mastering this skill is key for tackling higher‑level math with ease.
  5. Practice with Real‑Life Scenarios - Turn grocery shopping or game scorekeeping into a commutative playground by rearranging items or points. Seeing math in your daily routine makes the concept stick - and it's more fun than flashcards! Challenge friends to spot commutative moves in everyday life.
  6. Differentiate Commutative vs. Associative - While commutativity swaps order (a + b = b + a), associativity changes grouping ((a + b) + c = a + (b + c)). Think of commutative as a traffic lane swap and associative as choosing which two friends hang out first. Knowing the difference sharpens your problem‑solving toolkit.
  7. Utilize Mnemonic Devices - Remember "commute" in a city - cars change lanes but still reach the same destination, just like numbers in addition and multiplication. Craft your own catchy phrase or draw a tiny road map for equations. These memory hacks make studying a breeze and exams less stressful.
  8. Engage in Interactive Practice - Online quizzes and games turn the commutative property into an adventure, giving instant feedback and tracking your progress. Compete with classmates or beat your own high score to stay motivated. Active practice cements concepts faster than passive reading.
  9. Explore Visual Aids - Diagrams, animated videos, and colorful charts bring the commutative property to life by showing numbers swapping places in real time. These visual stories help your brain form lasting connections. Mix and match media for a richer learning experience.
  10. Review and Reflect Regularly - Build mastery by revisiting these points in short, spaced sessions - flashcards, doodles, or quick self‑quizzes work wonders. Reflect on your progress, celebrate small wins, and turn mistakes into learning moments. Consistency is the secret sauce to math success!
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