Elementary School Math Quiz: Apply Properties Of Multiplication
20 questions · exam conditions
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Apply Properties Of MultiplicationQuestion 1 of 20

Jake is solving 6×5×36 \times 5 \times 3. He decides to group the numbers differently to make it easier. Which two expressions will give Jake the same answer?

(6×5)×3(6 \times 5) \times 3 and 6×(5×3)6 \times (5 \times 3)
(6+5)×3(6 + 5) \times 3 and 6×(5+3)6 \times (5 + 3)
6×5+36 \times 5 + 3 and 6+5×36 + 5 \times 3
6×(5−3)6 \times (5 - 3) and (6−5)×3(6 - 5) \times 3
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Elementary School Math Quiz

Elementary School Math Quiz: Apply Properties Of Multiplication

Practice Apply Properties Of Multiplication in Elementary School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Apply Properties Of Multiplication, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Jake is solving 6×5×36 \times 5 \times 3. He decides to group the numbers differently to make it easier. Which two expressions will give Jake the same answer?

  1. (6×5)×3(6 \times 5) \times 3 and 6×(5×3)6 \times (5 \times 3) (correct answer)
  2. (6+5)×3(6 + 5) \times 3 and 6×(5+3)6 \times (5 + 3)
  3. 6×5+36 \times 5 + 3 and 6+5×36 + 5 \times 3
  4. 6×(5−3)6 \times (5 - 3) and (6−5)×3(6 - 5) \times 3
Explanation: Choice A shows the associative property of multiplication, where grouping doesn't change the product: (6 × 5) × 3 = 30 × 3 = 90, and 6 × (5 × 3) = 6 × 15 = 90. Choice B uses addition instead of multiplication in the groupings. Choice C changes multiplication to addition, giving different results. Choice D uses subtraction and gives different results: 6 × 2 = 12 vs. 1 × 3 = 3.

Question 2

If 7×9=637 \times 9 = 63, what is 9×79 \times 7?

  1. 79
  2. 72
  3. 16
  4. 63 (correct answer)
Explanation: 63 is correct because multiplying the same two numbers in either order gives the same product, so 9×7=7×9=639 \times 7 = 7 \times 9 = 63. 79 is incorrect; it combines the digits 7 and 9 rather than multiplying them. 72 is incorrect because it doesn't match the given product. 16 is incorrect; it comes from adding 9 and 7 instead of multiplying.

Question 3

Use the associative property to solve 4×2×54 \times 2 \times 5 efficiently.

  1. 4×(2×5)=4×10=144 \times (2 \times 5) = 4 \times 10 = 14
  2. 4×(2×5)=4×10=404 \times (2 \times 5) = 4 \times 10 = 40 (correct answer)
  3. (4+2)×5=30(4+2) \times 5 = 30
  4. (4×2)+5=13(4 \times 2) + 5 = 13
Explanation: This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using associative property as a strategy. The associative property of multiplication states the way factors are grouped doesn't change the product. (3×5)×2 = 3×(5×2). Both equal 30. Helpful for three or more factors: regroup to make easier calculations (2×5=10, then 10×3=30 is easier than 2×3=6, then 6×5=30). In this problem, we can solve 4×2×5 by regrouping to make it easier. The associative property helps by grouping 2×5 first to get 10, then multiply by 4. Choice A is correct because it regroups 4×(2×5) as 4×10=40 using associative property. This demonstrates proper use of the associative as a strategy. Choice D is incorrect because it has a calculation error, 4×10=40 not 14. This error occurs when students make computational mistakes within the property application. To help students apply properties: Explicitly teach and name properties with examples. Associative: Model with nested containers (boxes/bags/items). Show both groupings equal same total. Practice as strategies, not just as abstract properties: "How can associative property help you?" Connect to real situations. Watch for students who memorize property names but don't apply them strategically, or who make errors within the property application.

Question 4

If 6×8=486 \times 8 = 48, what is 8×68 \times 6?

  1. 14
  2. 46
  3. 48 (correct answer)
  4. 68
Explanation: 48 is correct because multiplying the same two numbers in either order gives the same product, so 8×6=6×8=488 \times 6 = 6 \times 8 = 48. 14 is incorrect; it doesn't match the given product. 46 is incorrect because it's close to 48 but not the actual value. 68 is incorrect; it combines the digits 6 and 8 rather than multiplying them.

Question 5

Maria knows that 4×9=364 \times 9 = 36. She wants to find 4×114 \times 11 using what she already knows. Which strategy shows the correct use of the distributive property?

  1. 4×11=4×(9+2)=(4×9)+(4×2)=36+8=444 \times 11 = 4 \times (9 + 2) = (4 \times 9) + (4 \times 2) = 36 + 8 = 44 (correct answer)
  2. 4×11=11×4=36+11=474 \times 11 = 11 \times 4 = 36 + 11 = 47
  3. 4×11=4×(9×2)=36×2=724 \times 11 = 4 \times (9 \times 2) = 36 \times 2 = 72
  4. 4×11=(4+9)×2=13×2=264 \times 11 = (4 + 9) \times 2 = 13 \times 2 = 26
Explanation: Choice A correctly uses the distributive property by breaking 11 into (9 + 2), then distributing the 4: 4 × (9 + 2) = (4 × 9) + (4 × 2) = 36 + 8 = 44. Choice B incorrectly adds 36 + 11 instead of using properties. Choice C mistakes 11 as 9 × 2 and uses an incorrect operation. Choice D incorrectly adds 4 + 9 and creates an unrelated expression.

Question 6

Ana is solving 7×5×47 \times 5 \times 4. She wants to make the calculation easier by changing how the numbers are grouped. Which grouping will give Ana the same answer as the original problem?

  1. (7×4)×5=35×5=175(7 \times 4) \times 5 = 35 \times 5 = 175
  2. (7×5)×4=35×4=140(7 \times 5) \times 4 = 35 \times 4 = 140 (correct answer)
  3. (7+5)×4=12×4=48(7 + 5) \times 4 = 12 \times 4 = 48
  4. 7×5+4=35+4=397 \times 5 + 4 = 35 + 4 = 39
Explanation: The correct regrouping is B, since the associative property lets Ana regroup the factors as (7x5)x4 = 35x4 = 140, the same value as the original 7x5x4. Choice A also multiplies throughout but contains an arithmetic error (7x4=28, not 35), giving a wrong product. Choices C and D change one of the operations to addition, which changes the value of the expression entirely.

Question 7

Use the distributive property to find 8×78 \times 7 by breaking apart 7.

  1. 8×7=8×(5+2)=8×5+8×2=40+16=568 \times 7 = 8 \times (5+2) = 8 \times 5 + 8 \times 2 = 40 + 16 = 56 (correct answer)
  2. 8×7=8×5+2=428 \times 7 = 8 \times 5 + 2 = 42
  3. 8×7=8×5+8×2=408 \times 7 = 8 \times 5 + 8 \times 2 = 40
  4. 8×7=8×5+2×2=40+4=448 \times 7 = 8 \times 5 + 2 \times 2 = 40 + 4 = 44
Explanation: Choice A is correct: 8 x 7 = 8 x (5+2) = 8 x 5 + 8 x 2 = 40 + 16 = 56. Choice B distributes to only the second term and drops the 8 x 5 part. Choice C finds both partial products but forgets to add them together. Choice D multiplies the second part by 2 instead of by 8, giving an incorrect partial product.

Question 8

Sarah is calculating 2×6×52 \times 6 \times 5. She notices that 6×5=306 \times 5 = 30 is easy to multiply. Which property allows Sarah to calculate (2×6)×5(2 \times 6) \times 5 or 2×(6×5)2 \times (6 \times 5) and get the same answer?

  1. Associative property of multiplication (correct answer)
  2. Commutative property of multiplication
  3. Distributive property of multiplication
  4. Identity property of multiplication
Explanation: Choice A is correct because the associative property allows us to change the grouping of factors without changing the product: (2 × 6) × 5 = 12 × 5 = 60, and 2 × (6 × 5) = 2 × 30 = 60. Choice B (commutative) deals with changing order, not grouping. Choice C (distributive) involves breaking apart one factor into a sum. Choice D (identity) involves multiplying by 1.

Question 9

If 7×5=357 \times 5 = 35, what is 7×67 \times 6?

  1. 67
  2. 40
  3. 42 (correct answer)
  4. 36
Explanation: 42 is correct because 7×6=7×5+7=35+7=427 \times 6 = 7 \times 5 + 7 = 35 + 7 = 42. 67 is incorrect; it isn't a valid product for 7×67 \times 6. 40 is incorrect because it adds only 5 instead of 7 to 35. 36 is incorrect because it adds just 1 instead of 7 to 35.

Question 10

Use the commutative property: if 6×8=486 \times 8 = 48, what is 8×68 \times 6?

  1. 68
  2. 46
  3. 48 (correct answer)
  4. 14
Explanation: This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using commutative property as a strategy. The commutative property of multiplication states the order of factors doesn't change the product. 6×4 = 4×6 = 24. Helpful when you know one fact (like 4×6) and need the reverse (6×4)—it's the same! In this problem, we need to find 8×6 given that 6×8=48. The commutative property helps by recognizing that switching the order gives the same product. Choice C is correct because it recognizes 8×6 = 6×8 by commutative property, so both equal 48. This demonstrates proper use of the commutative as a strategy. Choice B is incorrect because it claims 46, perhaps confusing with addition or another operation. This error occurs when students don't understand the property or make computational mistakes. To help students apply properties: Explicitly teach and name properties with examples. Commutative: Use arrays that can be rotated (6 rows of 4 = 4 rows of 6). Teach: "If you know one fact, you know its reverse!" Practice as strategies, not just as abstract properties: "How can commutative property help you?" Connect to real situations. Watch for students who memorize property names but don't apply them strategically, or who make errors within the property application.

Question 11

Which equation shows the commutative property (order doesn't change the product)?

  1. 6×4=4×66 \times 4 = 4 \times 6 (correct answer)
  2. (4×3)×2=4×(3×2)(4 \times 3) \times 2 = 4 \times (3 \times 2)
  3. 8×7=8×5+8×28 \times 7 = 8 \times 5 + 8 \times 2
  4. 7×5=7+57 \times 5 = 7+5
Explanation: This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using commutative property as a strategy. The commutative property of multiplication states the order of factors doesn't change the product. 6×4 = 4×6 = 24. Helpful when you know one fact (like 4×6) and need the reverse (6×4)—it's the same! In this problem, we need to identify which equation demonstrates that order doesn't change the product. The commutative property helps by showing equivalence when factors are swapped. Choice C is correct because it recognizes 6×4 = 4×6 by commutative property, so both equal 24. This demonstrates proper use of the commutative as a strategy. Choice D is incorrect because it claims 7×5 = 7+5, confusing multiplication with addition. This error occurs when students confuse properties. To help students apply properties: Explicitly teach and name properties with examples. Commutative: Use arrays that can be rotated (6 rows of 4 = 4 rows of 6). Teach: "If you know one fact, you know its reverse!" Practice as strategies, not just as abstract properties: "How can commutative property help you?" Connect to real situations. Watch for students who memorize property names but don't apply them strategically, or who make errors within the property application.

Question 12

Use the distributive property to find 6×96 \times 9 by thinking 9=10−19=10-1.

  1. 6×9=9×6=966 \times 9 = 9 \times 6 = 96
  2. 6×9=6×(10−1)=60−6=546 \times 9 = 6 \times (10-1) = 60-6 = 54 (correct answer)
  3. 6×9=6+9=156 \times 9 = 6+9 = 15
  4. 6×9=6×10−1=596 \times 9 = 6 \times 10 - 1 = 59
Explanation: Breaking 9 into 10 minus 1 gives 6 times 9 equals 6 times 10 minus 6 times 1, which is 60 minus 6, or 54. Choice A restates the numbers in reverse order but reaches an incorrect product without using the distributive breakdown. Choice C adds the two numbers instead of multiplying them. Choice D subtracts 1 directly from the product instead of subtracting 6, which is 6 times 1.

Question 13

You can think of 8 as 5 + 3. What is 7×87 \times 8?

  1. 48
  2. 56 (correct answer)
  3. 58
  4. 54
Explanation: 56 is correct because 7 times 8 equals 56. 48 is incorrect because that is the product of 6 and 8, not 7 and 8. 58 is incorrect because it is close to 56 but not the actual product. 54 is incorrect because it does not match 7 times 8.

Question 14

Kevin discovers that 6×9=546 \times 9 = 54. His teacher asks him to find 6×106 \times 10 using the distributive property and thinking of 10 as 9+19 + 1. What should Kevin's complete solution look like?

  1. 6×10=6×(9+1)=(6×9)+1=54+1=556 \times 10 = 6 \times (9+1) = (6 \times 9) + 1 = 54 + 1 = 55
  2. 6×10=6×(9+1)=(6×9)+(6×1)=54+6=606 \times 10 = 6 \times (9+1) = (6 \times 9) + (6 \times 1) = 54 + 6 = 60 (correct answer)
  3. 6×10=6×(9+1)=(6×9)×(6×1)=54×6=3246 \times 10 = 6 \times (9+1) = (6 \times 9) \times (6 \times 1) = 54 \times 6 = 324
  4. 6×10=6×(9+1)=(6+9)+(6+1)=15+7=226 \times 10 = 6 \times (9+1) = (6+9) + (6+1) = 15 + 7 = 22
Explanation: The correct solution is B, since the distributive property requires multiplying both parts of the sum (9 and 1) by 6 before adding: 6x9 + 6x1 = 54 + 6 = 60. Choice A only multiplies the 9 by 6 and then adds a bare 1 instead of 6x1. Choice C incorrectly multiplies the two partial products together instead of adding them. Choice D replaces multiplication with addition throughout, which isn't how the distributive property works.

Question 15

Carlos knows that 9×4=369 \times 4 = 36 and 9×3=279 \times 3 = 27. He wants to find 9×79 \times 7 using the distributive property. Which equation shows the correct way to break apart this problem?

  1. 9×7=9×(4×3)=9×12=1089 \times 7 = 9 \times (4 \times 3) = 9 \times 12 = 108
  2. 9×7=(9×4)×(9×3)=36×27=9729 \times 7 = (9 \times 4) \times (9 \times 3) = 36 \times 27 = 972
  3. 9×7=(9+4)+(9+3)=13+12=259 \times 7 = (9 + 4) + (9 + 3) = 13 + 12 = 25
  4. 9×7=9×(4+3)=36+27=639 \times 7 = 9 \times (4 + 3) = 36 + 27 = 63 (correct answer)
Explanation: D is correct because the distributive property breaks 7 into 4+3, multiplies each part by 9, then adds: 36 + 27 = 63. Choice A incorrectly multiplies 4 and 3 together inside the parentheses instead of adding them. Choice B incorrectly multiplies the two partial products instead of adding them. Choice C replaces multiplication with addition throughout, which isn't how the distributive property works.

Question 16

Use the distributive property: 6×9=6×(10−1)6 \times 9 = 6 \times (10-1). What is 6×96 \times 9?

  1. 51
  2. 69
  3. 54 (correct answer)
  4. 60
Explanation: Six times 10 is 60, and subtracting 6 times 1, or 6, gives 54. Choice A comes from a subtraction error. Choice B comes from an addition error instead of using the distributive property. Choice D stops after computing 6 times 10 without subtracting.

Question 17

Which regrouping correctly uses the associative property to solve 2×3×72 \times 3 \times 7?

  1. (2+3)×7=35(2+3) \times 7 = 35
  2. 2×(3+7)=202 \times (3+7) = 20
  3. (2×3)×7=42(2 \times 3) \times 7 = 42 (correct answer)
  4. (2×3)+7=13(2 \times 3) + 7 = 13
Explanation: Grouping 2 times 3 first, then multiplying by 7, gives 6 times 7, or 42. Choice A wrongly adds 2 and 3 instead of multiplying them. Choice B wrongly adds 3 and 7 instead of keeping the multiplication grouping. Choice D wrongly adds 7 instead of multiplying by it.

Question 18

Use a near fact: 9×8=10×8−1×89 \times 8 = 10 \times 8 - 1 \times 8. What is 9×89 \times 8?

  1. 72 (correct answer)
  2. 78
  3. 80
  4. 88
Explanation: Ten times 8 is 80, and subtracting 1 times 8, or 8, gives 72. Choice B comes from a subtraction error. Choice C stops after computing 10 times 8 without subtracting. Choice D comes from adding instead of using the near-fact strategy correctly.

Question 19

Which expression correctly uses the distributive property to find 7×67 \times 6, given that 7×5=357 \times 5 = 35?

  1. 7×6=7×5+7×1=35+7=427 \times 6 = 7 \times 5 + 7 \times 1 = 35 + 7 = 42 (correct answer)
  2. 7×6=7×5−7×1=35−7=287 \times 6 = 7 \times 5 - 7 \times 1 = 35 - 7 = 28
  3. 7×6=7×5+1=367 \times 6 = 7 \times 5 + 1 = 36
  4. 7×6=7+6=137 \times 6 = 7 + 6 = 13
Explanation: Breaking 6 into 5+1, 7 x 6 = 7 x 5 + 7 x 1 = 35 + 7 = 42, so Choice A is correct. Choice B subtracts the extra group instead of adding it. Choice C adds only 1 instead of 7 x 1, forgetting to multiply the extra group by 7. Choice D adds 7 and 6 instead of multiplying them, confusing the two operations entirely.

Question 20

Which strategy correctly breaks apart the numbers to solve 7×97 \times 9?

  1. 7×9=9×77 \times 9 = 9 \times 7
  2. 7×9=7×(10−1)=70−77 \times 9 = 7 \times (10-1) = 70 - 7 (correct answer)
  3. 7×9=7+97 \times 9 = 7 + 9
  4. 7×9=(7+9)×17 \times 9 = (7+9) \times 1
Explanation: Breaking 9 into 10 minus 1 is correct because 7 times 9 equals 7 times 10 minus 7, which is 63. Reversing the order of the factors is incorrect because it does not break either number apart. Adding 7 and 9 is incorrect because it replaces multiplication with addition. Adding the numbers first and multiplying by 1 is incorrect because it also replaces multiplication with addition.