Worksheet reviewing mathematical properties with multiple-choice questions.
A worksheet titled "Review of Properties" with seven multiple-choice questions testing understanding of mathematical properties such as commutative, associative, distributive, and identity properties.
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Step-by-step solution for: Multiplication Properties: Five Worksheets by Deb Hanson worksheets library
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Show Answer Key & Explanations
Step-by-step solution for: Multiplication Properties: Five Worksheets by Deb Hanson worksheets library
Thank you for uploading the image. I’ll solve each question step by step, explaining which property is being shown and why.
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> Commutative Property of Multiplication:
> *a × b = b × a* — The order of factors doesn’t change the product.
Let’s check the options:
- A. 3 × (2 × 4) = (3 × 2) × 4 → This shows associative property (grouping changes).
- B. 2 × 3 = 4 + 2 → Not even equal! 6 ≠ 6? Wait, 2×3=6, 4+2=6 — but this is mixing operations; not a property of multiplication.
- C. 3 × 2 = 2 × 3 → YES! Same numbers, order swapped, same result → Commutative.
- D. 2 × 3 = 3 × 2 → Also correct! Same as C.
Wait — both C and D are identical? Probably a typo in the image. Assuming they’re meant to be different, but as written, C and D are the same.
✔ Correct Answer: C or D — since both say 3×2 = 2×3.
*(If forced to pick one, choose C — it’s listed first.)*
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> Associative Property of Addition:
> *(a + b) + c = a + (b + c)* — Grouping changes, sum stays same.
Options:
- A. 3 × (8 × 8) = (3 × 8) × 8 → Multiplication — not addition.
- B. 5 + (3 + 8) = 3 + 8 → Left side: 5+11=16, right: 11 → Not equal.
- C. 5 + (3 + 8) = 3 + 8 → Same as B — wrong.
- D. 2 + (7 + 9) = (2 + 7) + 9 → YES! Left: 2+16=18, Right: 9+9=18 → Same result, grouping changed → Associative Property of Addition.
✔ Correct Answer: D
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> Identity Property of Multiplication:
> *a × 1 = a* — Multiplying by 1 leaves number unchanged.
Options:
- A. 9 × 1 = 9 → YES! Perfect example.
- B. 2 + 1 = 1 + 2 → Commutative property of addition.
- C. 9 × 0 = 0 → Zero property, not identity.
- D. 9 × 2 = (9 × 2) × 5 → Not true unless 5=1 — nonsense.
✔ Correct Answer: A
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> Distributive Property:
> *a × (b + c) = a×b + a×c*
Options:
- A. 2 × (8 + 7) = n → Incomplete — no right side shown.
- B. 2 × (8 + 7) = n → Same as A — incomplete.
- C. 2 × (8 + 7) = 2 × 8 + 2 × 7 → YES! Classic distributive property.
- D. 2 × (8 + 7) = n → Again, incomplete.
✔ Correct Answer: C
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> Commutative Property of Addition:
> *a + b = b + a*
Options:
- A. 3 + 4 = 4 + 3 → YES! Order swapped, same sum.
- B. 3 + (5 + 6) = (3 + 5) + 6 → Associative property.
- C. 5 + 0 = 5 → Identity property.
- D. 3 × (4 + 27) → Not even an equation — just expression.
✔ Correct Answer: A
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> Identity Property of Addition:
> *a + 0 = a*
Options:
- A. 3 × 0 = 0 → Multiplication zero property.
- B. 3 + 0 = 3 → YES! Adding zero doesn’t change value.
- C. 3 × 1 = 3 → Identity property of multiplication.
- D. 3 + 5 = 8 → Just basic addition — no property shown.
✔ Correct Answer: B
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> Associative Property of Multiplication:
> *(a × b) × c = a × (b × c)*
Options:
- A. 7 × (4 × 2) = (7 × 4) × 2 → YES! Grouping changed, same result → Associative.
- B. 7 × (4 + 2) = (7 × 4) + 2 → Distributive would be 7×4 + 7×2 — this is incorrect.
- C. 7 × (4 × 2) = 7 × (2 × 4) → This is commutative within the parentheses — not associative.
- D. 7 × (4 × 2) = 7 × (2 × 4) → Same as C — commutative.
✔ Correct Answer: A
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## ✔ Final Answers:
1. C (or D — they’re identical)
2. D
3. A
4. C
5. A
6. B
7. A
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Let me know if you’d like a printable version or further explanation on any property!
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1. Which of the following equations is showing the commutative property of multiplication?
> Commutative Property of Multiplication:
> *a × b = b × a* — The order of factors doesn’t change the product.
Let’s check the options:
- A. 3 × (2 × 4) = (3 × 2) × 4 → This shows associative property (grouping changes).
- B. 2 × 3 = 4 + 2 → Not even equal! 6 ≠ 6? Wait, 2×3=6, 4+2=6 — but this is mixing operations; not a property of multiplication.
- C. 3 × 2 = 2 × 3 → YES! Same numbers, order swapped, same result → Commutative.
- D. 2 × 3 = 3 × 2 → Also correct! Same as C.
Wait — both C and D are identical? Probably a typo in the image. Assuming they’re meant to be different, but as written, C and D are the same.
✔ Correct Answer: C or D — since both say 3×2 = 2×3.
*(If forced to pick one, choose C — it’s listed first.)*
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2. Which of the following equations is showing the associative property of addition?
> Associative Property of Addition:
> *(a + b) + c = a + (b + c)* — Grouping changes, sum stays same.
Options:
- A. 3 × (8 × 8) = (3 × 8) × 8 → Multiplication — not addition.
- B. 5 + (3 + 8) = 3 + 8 → Left side: 5+11=16, right: 11 → Not equal.
- C. 5 + (3 + 8) = 3 + 8 → Same as B — wrong.
- D. 2 + (7 + 9) = (2 + 7) + 9 → YES! Left: 2+16=18, Right: 9+9=18 → Same result, grouping changed → Associative Property of Addition.
✔ Correct Answer: D
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3. Which of the following equations is showing the identity property of multiplication?
> Identity Property of Multiplication:
> *a × 1 = a* — Multiplying by 1 leaves number unchanged.
Options:
- A. 9 × 1 = 9 → YES! Perfect example.
- B. 2 + 1 = 1 + 2 → Commutative property of addition.
- C. 9 × 0 = 0 → Zero property, not identity.
- D. 9 × 2 = (9 × 2) × 5 → Not true unless 5=1 — nonsense.
✔ Correct Answer: A
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4. Which of the following equations is showing the distributive property?
> Distributive Property:
> *a × (b + c) = a×b + a×c*
Options:
- A. 2 × (8 + 7) = n → Incomplete — no right side shown.
- B. 2 × (8 + 7) = n → Same as A — incomplete.
- C. 2 × (8 + 7) = 2 × 8 + 2 × 7 → YES! Classic distributive property.
- D. 2 × (8 + 7) = n → Again, incomplete.
✔ Correct Answer: C
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5. Which of the following equations is showing the commutative property of addition?
> Commutative Property of Addition:
> *a + b = b + a*
Options:
- A. 3 + 4 = 4 + 3 → YES! Order swapped, same sum.
- B. 3 + (5 + 6) = (3 + 5) + 6 → Associative property.
- C. 5 + 0 = 5 → Identity property.
- D. 3 × (4 + 27) → Not even an equation — just expression.
✔ Correct Answer: A
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6. Which of the following equations is showing the identity property of addition?
> Identity Property of Addition:
> *a + 0 = a*
Options:
- A. 3 × 0 = 0 → Multiplication zero property.
- B. 3 + 0 = 3 → YES! Adding zero doesn’t change value.
- C. 3 × 1 = 3 → Identity property of multiplication.
- D. 3 + 5 = 8 → Just basic addition — no property shown.
✔ Correct Answer: B
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7. Which of the following equations is showing the associative property of multiplication?
> Associative Property of Multiplication:
> *(a × b) × c = a × (b × c)*
Options:
- A. 7 × (4 × 2) = (7 × 4) × 2 → YES! Grouping changed, same result → Associative.
- B. 7 × (4 + 2) = (7 × 4) + 2 → Distributive would be 7×4 + 7×2 — this is incorrect.
- C. 7 × (4 × 2) = 7 × (2 × 4) → This is commutative within the parentheses — not associative.
- D. 7 × (4 × 2) = 7 × (2 × 4) → Same as C — commutative.
✔ Correct Answer: A
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## ✔ Final Answers:
1. C (or D — they’re identical)
2. D
3. A
4. C
5. A
6. B
7. A
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Let me know if you’d like a printable version or further explanation on any property!
Parent Tip: Review the logic above to help your child master the concept of properties of multiplication worksheet grade 5.
