Let's solve each of the addition problems using the
commutative and
associative properties of addition, as instructed.
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🔁 Commutative Property:
> $ a + b = b + a $
This means the order of numbers doesn't matter.
🔄 Associative Property:
> $ (a + b) + c = a + (b + c) $
This means you can group numbers in different ways without changing the sum.
We’ll use these to simplify and solve the problems efficiently.
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✔ Now, let’s solve each problem:
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1.
2 + 8 = ___
→ $ 2 + 8 = 10 $
*(Simple addition)*
Answer: 10
2.
4 + 11 = ___
→ $ 4 + 11 = 15 $
Answer: 15
3.
6 + 4 + 6 = ___
Use associative property: Group $ 6 + 4 = 10 $, then $ 10 + 6 = 16 $
Or commutative: Rearranged as $ 6 + 6 + 4 = 12 + 4 = 16 $
Answer: 16
4.
7 + 12 = ___
→ $ 7 + 12 = 19 $
Answer: 19
5.
3 + 7 + 2 = ___
Use associative: $ (3 + 7) + 2 = 10 + 2 = 12 $
Or rearrange: $ 3 + 2 + 7 = 5 + 7 = 12 $
Answer: 12
6.
5 + 12 = ___
→ $ 5 + 12 = 17 $
Answer: 17
7.
5 + 1 + 5 = ___
Use associative: $ (5 + 5) + 1 = 10 + 1 = 11 $
Answer: 11
8.
2 + 9 + 8 = ___
Rearrange using commutative: $ 2 + 8 + 9 = 10 + 9 = 19 $
Or $ (2 + 8) + 9 = 10 + 9 = 19 $
Answer: 19
9.
11 + 7 = ___
→ $ 11 + 7 = 18 $
Answer: 18
10.
8 + 9 = ___
→ $ 8 + 9 = 17 $
Answer: 17
11.
2 + 5 + 8 = ___
Rearrange: $ 2 + 8 + 5 = 10 + 5 = 15 $
Or $ (2 + 5) + 8 = 7 + 8 = 15 $
Answer: 15
12.
9 + 4 + 1 = ___
Use associative: $ 9 + (4 + 1) = 9 + 5 = 14 $
Or rearrange: $ 9 + 1 + 4 = 10 + 4 = 14 $
Answer: 14
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✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1. 2 + 8 |
10 |
| 2. 4 + 11 |
15 |
| 3. 6 + 4 + 6 |
16 |
| 4. 7 + 12 |
19 |
| 5. 3 + 7 + 2 |
12 |
| 6. 5 + 12 |
17 |
| 7. 5 + 1 + 5 |
11 |
| 8. 2 + 9 + 8 |
19 |
| 9. 11 + 7 |
18 |
| 10. 8 + 9 |
17 |
| 11. 2 + 5 + 8 |
15 |
| 12. 9 + 4 + 1 |
14 |
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🎯 Summary:
- We used the
commutative property to reorder numbers (e.g., 2 + 8 + 5 becomes 2 + 8 + 5).
- We used the
associative property to group numbers that make tens (like 2 + 8 = 10), making mental math easier.
- These strategies help simplify multi-number addition.
Let me know if you'd like this worksheet filled out digitally or printed!
Parent Tip: Review the logic above to help your child master the concept of commutative property worksheet for 2nd grade.
