Let’s go through each problem one by one. We’re looking for the property that makes the two sides of the equation equal — meaning, why is it okay to rewrite the expression this way?
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Problem 1:
(1 + 3) + 9 = 1 + (3 + 9)
This shows grouping changing in addition — but the order of numbers stays the same. That’s the
Associative Property of Addition.
✔ Correct answer:
Associative Property of Addition
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Problem 2:
(5 + 8) + 7 = 5 + (8 + 7)
Same as above — parentheses move, but it’s still all addition and same numbers. Again,
Associative Property of Addition.
✔ Correct answer:
Associative Property of Addition
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Problem 3:
(7 + 3) + 2 = 7 + (3 + 2)
Again, just regrouping addends — no change in order. Still
Associative Property of Addition.
✔ Correct answer:
Associative Property of Addition
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Problem 4:
(6 + 9) + 2 = 6 + (9 + 2)
Same pattern — moving parentheses around in an addition problem. Still
Associative Property of Addition.
✔ Correct answer:
Associative Property of Addition
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Problem 5:
6 + 2 = 2 + 6
Here, the order of the numbers changed — not the grouping. This is swapping places → that’s the
Commutative Property of Addition.
✔ Correct answer:
Commutative Property of Addition
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Problem 6:
(5 · 3) · 9 = 5 · (3 · 9)
Now we have multiplication (the dot “·” means multiply). The grouping changes, but order stays same → that’s
Associative Property of Multiplication.
✔ Correct answer:
Associative Property of Multiplication
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Final 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
Parent Tip: Review the logic above to help your child master the concept of identify the properties of mathematics worksheet.
