Let's solve each problem by identifying the
multiplication property used in each equation. Here are the common properties of multiplication:
1.
Commutative Property: $ a \times b = b \times a $
→ Order doesn't matter.
2.
Associative Property: $ (a \times b) \times c = a \times (b \times c) $
→ Grouping doesn’t matter.
3.
Identity Property: $ a \times 1 = a $
→ Multiplying by 1 leaves the number unchanged.
4.
Zero Property: $ a \times 0 = 0 $
→ Any number times zero is zero.
5.
Distributive Property: $ (a + b) \times c = (a \times c) + (b \times c) $
→ Multiply a sum by distributing the multiplier.
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Now, let’s go through each equation:
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1. $ 2 \times (5 \times 2) = (2 \times 5) \times 2 $
→ The grouping changes: from $ 2 \times (5 \times 2) $ to $ (2 \times 5) \times 2 $.
✔ Associative Property
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2. $ 2 \times 7 = 7 \times 2 $
→ The order of numbers is switched.
✔ Commutative Property
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3. $ 10 \times 1 = 10 $
→ Multiplying by 1 keeps the number the same.
✔ Identity Property
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4. $ 2 \times 0 = 0 $
→ Any number times zero equals zero.
✔ Zero Property
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5. $ 4 \times (8 \times 6) = (4 \times 8) \times 6 $
→ Grouping changes: from $ 4 \times (8 \times 6) $ to $ (4 \times 8) \times 6 $.
✔ Associative Property
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6. $ 4 \times 8 = 8 \times 4 $
→ Numbers are swapped in order.
✔ Commutative Property
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7. $ (3 + 4) \times 6 = (3 \times 6) + (4 \times 6) $
→ A sum is multiplied by a number, and it's distributed.
✔ Distributive Property
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8. $ 5 \times 0 = 0 $
→ Any number times zero is zero.
✔ Zero Property
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9. $ 11 \times 1 = 11 $
→ Multiplying by 1 gives the original number.
✔ Identity Property
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10. $ 12 \times (14 \times 11) = (12 \times 14) \times 11 $
→ Grouping changes: $ 12 \times (14 \times 11) $ becomes $ (12 \times 14) \times 11 $.
✔ Associative Property
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11. $ 20 \times 0 = 0 $
→ Again, any number times zero is zero.
✔ Zero Property
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12. $ 31 \times 1 = 31 $
→ Multiplying by 1 keeps the number the same.
✔ Identity Property
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✔ Final Answers:
1.
Associative Property
2.
Commutative Property
3.
Identity Property
4.
Zero Property
5.
Associative Property
6.
Commutative Property
7.
Distributive Property
8.
Zero Property
9.
Identity Property
10.
Associative Property
11.
Zero Property
12.
Identity Property
Let me know if you'd like this formatted for printing or as a worksheet!
Parent Tip: Review the logic above to help your child master the concept of properties worksheet.
