Let's solve each problem step by step and identify the correct property that justifies each equation. We’ll go through each question and explain why the chosen property is correct.
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1.
(1 + 3) + 9 = 1 + (3 + 9)
- This shows that the grouping of numbers in addition changes, but the result stays the same.
- The
Associative Property of Addition states:
$$(a + b) + c = a + (b + c)$$
- Here, we are changing the grouping of the addends.
✔ Answer: ✔ Associative Property of Addition
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2.
(5 + 8) + 7 = 5 + (8 + 7)
- Again, the grouping of numbers in addition is changed.
- Same logic as above — it’s about how parentheses are moved in an addition expression.
✔ Answer: ✔ Associative Property of Addition
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3.
(7 + 3) + 2 = 7 + (3 + 2)
- Once more, this involves changing the grouping of addends.
- Still addition, and the order of operations is preserved; only grouping changes.
✔ Answer: ✔ Associative Property of Addition
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4.
(6 + 9) + 2 = 6 + (9 + 2)
- Grouping of addends is changed again.
- No change in order, just regrouping.
✔ Answer: ✔ Associative Property of Addition
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5.
6 + 2 = 2 + 6
- Here, the
order of the numbers is switched.
- The
Commutative Property of Addition states:
$$a + b = b + a$$
- This is about swapping the order of numbers.
✔ Answer: ✔ Commutative Property of Addition
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6.
(5 · 3) · 9 = 5 · (3 · 9)
- This time, we’re dealing with multiplication.
- The grouping of numbers is changed: from multiplying (5×3) first to (3×9) first.
- The
Associative Property of Multiplication states:
$$(a \cdot b) \cdot c = a \cdot (b \cdot c)$$
✔ Answer: ✔ Associative Property of Multiplication
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✔ Final Answers:
| Question | Correct Answer |
|--------|----------------|
| 1 | Associative Property of Addition |
| 2 | Associative Property of Addition |
| 3 | Associative Property of Addition |
| 4 | Associative Property of Addition |
| 5 | Commutative Property of Addition |
| 6 | Associative Property of Multiplication |
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🔍 Summary of Properties:
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Associative Property of Addition: Changing grouping doesn’t affect sum → $(a + b) + c = a + (b + c)$
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Associative Property of Multiplication: Changing grouping doesn’t affect product → $(a \cdot b) \cdot c = a \cdot (b \cdot c)$
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Commutative Property of Addition: Order doesn’t matter → $a + b = b + a$
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Commutative Property of Multiplication: Order doesn’t matter → $a \cdot b = b \cdot a$
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Distributive Property: Involves both addition and multiplication → $a(b + c) = ab + ac$
> Note: None of these problems involve the Distributive Property or Commutative Property of Multiplication directly.
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Parent Tip: Review the logic above to help your child master the concept of algebraic properties worksheets.
