Let's solve each multiplication sentence and identify the correct
property of multiplication shown. We are to use the following abbreviations:
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CPM = Commutative Property of Multiplication
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APM = Associative Property of Multiplication
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ZPM = Zero Property of Multiplication
-
IPM = Identity Property of Multiplication
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1.) 2 × 3 = 3 × 2
Answer: CPM
→ The order of the numbers is switched, but the product remains the same. This is the
Commutative Property.
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2.) 0 × 7 = 0
Answer: ZPM
→ Any number multiplied by zero equals zero. This is the
Zero Property.
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3.) 1 × 6 = 6
Answer: IPM
→ Multiplying any number by 1 gives the same number. This is the
Identity Property.
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4.) 2 × (4 × 5) = (2 × 4) × 5
Answer: APM
→ The grouping of numbers changes, but the product stays the same. This is the
Associative Property.
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5.) 8 × 5 = 5 × 8
Answer: CPM
→ The order of the factors is reversed. This is the
Commutative Property.
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6.) (9 × 2) × 4 = 9 × (2 × 4)
Answer: APM
→ The grouping of the numbers changes, but not the order. This is the
Associative Property.
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7.) 12 × 0 = 0
Answer: ZPM
→ Any number times zero is zero. This is the
Zero Property.
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8.) 37 × 1 = 37
Answer: IPM
→ Multiplying by 1 leaves the number unchanged. This is the
Identity Property.
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9.) 2 × 7 = 7 × 2
Answer: CPM
→ Order is changed; this is the
Commutative Property.
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10.) 5 × (2 × 3) = (5 × 2) × 3
Answer: APM
→ Grouping changes: (2×3) becomes (5×2), but the overall structure shows regrouping. This is the
Associative Property.
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✔ Final Answers:
1. CPM
2. ZPM
3. IPM
4. APM
5. CPM
6. APM
7. ZPM
8. IPM
9. CPM
10. APM
Let me know if you'd like a brief explanation for each!
Parent Tip: Review the logic above to help your child master the concept of properties of multiplication worksheet grade.
