Here is the solution to the worksheet, with explanations for each problem:
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1. 57 × (85 + 13) = 57 × 85 + 57 × 13
✔ Distributive Property
*Explanation:* The distributive property states that multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products:
a × (b + c) = a × b + a × c
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2. (13 + 84) + 53 = 13 + (84 + 53)
✔ Associative Property of Addition
*Explanation:* The associative property says that when adding three or more numbers, the way you group them doesn’t change the sum:
(a + b) + c = a + (b + c)
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3. 6 × (19 + 12) = 6 × 19 + 6 × 12
✔ Distributive Property
*Explanation:* Again, this shows multiplication distributed over addition:
a × (b + c) = a × b + a × c
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4. 41 + 77 = 77 + 41
✔ Commutative Property of Addition
*Explanation:* The commutative property says that changing the order of addends doesn’t change the sum:
a + b = b + a
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5. (10 + 20) + 30 = 10 + (20 + 30)
✔ Associative Property of Addition
*Explanation:* Grouping changes, but the sum stays the same.
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6. 23 + 42 = 42 + 23
✔ Commutative Property of Addition
*Explanation:* Order of addends is switched — classic commutative property.
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7. (12 + 55) + 61 = 12 + (55 + 61)
✔ Associative Property of Addition
*Explanation:* Grouping of addends is rearranged without changing the result.
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8. (73 + 32) + 57 = 73 + (32 + 57)
✔ Associative Property of Addition
*Explanation:* Same as above — regrouping addends.
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9. 62 × (94 + 5) = 62 × 94 + 62 × 5
✔ Distributive Property
*Explanation:* Multiplication distributes over the addition inside the parentheses.
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10. 81 + 9 = 9 + 81
✔ Commutative Property of Addition
*Explanation:* Switching the order of the two numbers being added.
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✔ Final Answers Summary:
1. Distributive
2. Associative
3. Distributive
4. Commutative
5. Associative
6. Commutative
7. Associative
8. Associative
9. Distributive
10. Commutative
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Parent Tip: Review the logic above to help your child master the concept of commutative associative distributive property worksheet.
