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Quizzes > Mathematics > Basic Math & Arithmetic

Think You Know the Properties of Addition and Multiplication? Test Yourself!

Identify associative property equations and commutative property examples in our quick quiz - dive in now!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for a math skills quiz on associative and commutative properties on sky blue background

Ready to unlock the associative property of addition and see arithmetic in a new light? Our free properties of addition and multiplication quiz is designed to test your skills. You'll uncover why regrouping numbers never alters the sum and apply these rules in everyday problem-solving. Instant feedback keeps you on track as you master each concept. You'll learn to identify associative property equation with ease, spot commutative property examples, and reinforce your understanding through engaging associative and commutative properties practice. Whether you're prepping for exams or looking for fun math challenges, take our interactive addition quiz or try a quick quiz for multiplication - dive in today and conquer the concepts!

Which equation represents the associative property of addition?
2+(3×4) = (2+3)×4
(2+3)+4 = 2+(3+4)
2+3 = 3+2
2+0 = 2
The associative property of addition states that changing the grouping of addends does not change the sum. In both (2+3)+4 and 2+(3+4), the result is 9. This property is different from commutativity, which allows swapping the order of addends. Learn more.
Which equation illustrates the commutative property of addition?
5 + (9 + 2) = (5 + 9) + 2
(5 + 9) + 2 = 5 + (9 + 2)
5 + 0 = 5
5 + 9 = 9 + 5
The commutative property of addition allows the order of addends to be swapped without changing the sum, as shown by 5+9=9+5. Unlike associativity, commutativity focuses solely on order, not grouping. This holds true for all real numbers under addition. Learn more.
Which expression demonstrates the associative property of multiplication?
3 × 4 = 4 × 3
(3 × 4) × 5 = 3 × (4 × 5)
(3 + 4) × 5 = 3 + (4 × 5)
3 × (4 + 5) = (3 × 4) + 5
The associative property of multiplication states that the way factors are grouped does not affect the product. Both (3×4)×5 and 3×(4×5) equal 60. Commutativity deals with swapping order, while associativity deals with regrouping. Learn more.
Complete the equation using the associative property: 7 + (2 + 6) = (7 + 2) + __.
15
7
2
6
The associative property allows you to move parentheses without changing the sum. Regrouping 7+(2+6) to (7+2)+6 yields the same result, so the blank must be 6. This property applies to any real numbers under addition. Learn more.
Using the associative property, which is an equivalent grouping for (8 + 15) + 7?
8 + (15 + 7)
(8 + 7) + 15
7 + (8 + 15)
(15 + 8) + 7
The associative property allows you to regroup addends without changing the sum. From (8+15)+7, you can move the parentheses to form 8+(15+7). Other options involve changing order, which is commutativity, not pure associativity. Learn more.
True or False: The associative property applies to subtraction as well as addition.
False
True
Subtraction is not associative because (a - b) - c generally does not equal a - (b - c). While addition allows regrouping freely, subtraction changes value when parentheses move. Learn more.
Evaluate 5 + (9 + 6).
19
21
18
20
By the associative property, 5+(9+6) = (5+9)+6 = 14+6 = 20. Regrouping addends does not affect the final sum. Learn more.
Use the associative property to simplify 1 + (99 + 2).
103
100
102
101
The associative property lets you rewrite 1+(99+2) as (1+99)+2. Calculating inside the first parentheses gives 100+2 = 102. This regrouping makes arithmetic easier without changing the result. Learn more.
True or False: The associative property applies to both addition and multiplication for all real numbers.
False
True
Both addition and multiplication are associative over the real numbers, meaning (a+b)+c = a+(b+c) and (a×b)×c = a×(b×c) for any real a, b, c. This does not extend to operations like subtraction or division. Learn more.
Given the sum (4 + x) + (3 + 2), which grouping simplifies mental calculation using associativity and commutativity?
(4 + 3) + (x + 2)
((4 + x) + 3) + 2
4 + (x + (3 + 2))
(4 + (x + 3)) + 2
By first using commutativity to pair 4 with 3 and x with 2, then associativity to group them, you get (4+3)+(x+2). This yields 7 + (x+2), simplifying mental math. Learn more.
Which property is illustrated by the equality (7 × 2) × 5 = 7 × (2 × 5)?
Commutative property of multiplication
Associative property of multiplication
Identity property
Distributive property
The equation (7×2)×5 = 7×(2×5) shows that regrouping factors does not affect the product, which is the associative property of multiplication. Commutativity would swap the order, not the grouping. Learn more.
Consider the expression 12 + (23 + (34 + 45)). Which rearrangement using the associative and commutative properties leads to the easiest mental calculation?
((12 + 23) + 34) + 45
(45 + 12) + (34 + 23)
12 + (23 + 34) + 45
(12 + 23) + (34 + 45)
By using commutativity to pair 45 with 12 and 34 with 23, then associativity to group them, you get (45+12)+(34+23) = 57+57 = 114. This symmetric grouping simplifies the mental addition. Learn more.
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Study Outcomes

  1. Apply the associative property of addition -

    Regroup addends in multi-step sums to simplify calculations, demonstrating how the associative property of addition maintains the same total regardless of grouping.

  2. Identify associative property equations -

    Spot and select equations that explicitly show the associative property of addition, reinforcing your ability to recognize proper groupings in addition expressions.

  3. Differentiate between associative and commutative properties -

    Distinguish how regrouping addends (associative) differs from swapping them (commutative) to deepen your understanding of fundamental math rules.

  4. Analyze commutative property examples -

    Examine addition and multiplication equations to confirm when rearranging numbers or factors preserves the result, using clear commutative property examples.

  5. Evaluate properties of addition and multiplication -

    Use targeted practice from this properties of addition and multiplication quiz to solve expressions accurately and check your mastery of both properties.

  6. Strengthen problem-solving confidence -

    Apply associative and commutative properties practice to build speed and accuracy, boosting your confidence in manipulating numbers during more complex calculations.

Cheat Sheet

  1. Definition of the Associative Property of Addition -

    The associative property of addition states that for any real numbers a, b, and c, (a + b) + c = a + (b + c). This grouping concept shows that no matter how you parenthesize sums, the result remains unchanged, as illustrated by (2+3)+4 = 2+(3+4) = 9 (Khan Academy).

  2. Distinguishing Associative vs. Commutative Properties -

    While the associative property deals with how numbers are grouped, the commutative property focuses on order: a + b = b + a (National Council of Teachers of Mathematics). For example, 4 + 5 = 5 + 4 demonstrates commutativity, whereas (4 + 5) + 6 = 4 + (5 + 6) showcases associativity.

  3. Using Associativity for Mental Math -

    Regrouping numbers into friendly pairs simplifies calculations, such as (18 + 2) + 7 = 18 + (2 + 7) = 27, speeding up mental addition (American Mathematical Society). Adopting this strategy boosts both speed and accuracy when tackling longer sums.

  4. Extending Associative Property to Multiplication -

    The associative rule also applies to multiplication: (a × b) × c = a × (b × c), so (2×3)×4 = 2×(3×4) = 24 (MIT OpenCourseWare). Recognizing this parallel across operations strengthens your overall number sense.

  5. Memory Aids and Practice Strategies -

    Use the mnemonic "Associate to Fascinate" to remember that regrouping numbers doesn't alter sums; picture friends forming circles in different orders while the total stays the same. Regular quizzes and flashcards from the University of Cambridge Faculty of Education help solidify your understanding of associative and commutative property examples.

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