Students fill in the blank to identify which property of operations is shown in each equation.

You’ve uploaded a worksheet with 20 algebraic expressions, and the task is to identify which algebraic law (property) is being demonstrated in each. The most common laws are:

- Commutative Law: Order doesn’t matter → `a + b = b + a` or `a × b = b × a`
- Associative Law: Grouping doesn’t matter → `(a + b) + c = a + (b + c)` or `(a × b) × c = a × (b × c)`
- Distributive Law: Multiplication distributes over addition → `a × (b + c) = a×b + a×c`

Let’s go through each one and fill in the correct law.

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✔ Completed Worksheet with Explanations:

1. 2 × 3 = 3 × 2 → Commutative Law (Multiplication)
*Explanation:* Changing the order of multiplication doesn’t change the result.

2. (6 + 9) + 8 = 6 + (9 + 8) → Associative Law (Addition)
*Explanation:* Changing the grouping of addends doesn’t change the sum.

3. 5 + 12 = 12 + 5 → Commutative Law (Addition)
*Explanation:* Order of addition doesn’t matter.

4. 6 × 8 + 4 × 8 = (6 + 4) × 8 → Distributive Law
*Explanation:* Common factor (8) is factored out — this is the reverse of distribution: `a×c + b×c = (a+b)×c`.

5. 5 × 11 + 12 × 11 = 17 × 11 → Distributive Law
*Explanation:* `5×11 + 12×11 = (5+12)×11 = 17×11` — again, factoring out the common factor 11.

6. (7 × 3) × 9 = 7 × (3 × 9) → Associative Law (Multiplication)
*Explanation:* Grouping of factors doesn’t affect the product.

7. (3 × 5) × 11 = 3 × (5 × 11) → Associative Law (Multiplication)
*Explanation:* Same as above — regrouping multiplication.

8. (8 × 12) + 9 × 12 = (8 + 9) × 12 → Distributive Law
*Explanation:* Factoring out 12: `8×12 + 9×12 = (8+9)×12`.

9. 4 × 2 = 2 × 4 → Commutative Law (Multiplication)
*Explanation:* Swapping order of multipliers.

10. 10 × 7 + 9 × 7 = (10 + 9) × 7 → Distributive Law
*Explanation:* Factoring out 7.

11. (11 × 4) × 8 = 11 × (4 × 8) → Associative Law (Multiplication)
*Explanation:* Regrouping multiplication.

12. 6 ÷ 3 = 3 ÷ 6 → ❗ This is FALSE — not a valid law!
*Explanation:* Division is not commutative. `6÷3 = 2`, but `3÷6 = 0.5`. This might be a trick question or error. If forced to label, you could say “None — incorrect statement”, but if the worksheet expects a law, it’s likely a mistake.

⚠️ *Note: Since this is mathematically false, it does NOT demonstrate any valid algebraic law.*

13. 5 × 2 + 3 × 2 = 8 × 2 → Distributive Law
*Explanation:* `5×2 + 3×2 = (5+3)×2 = 8×2`.

14. 9 + (4 + 10) = (9 + 4) + 10 → Associative Law (Addition)
*Explanation:* Regrouping addends.

15. 18 × 6 = 7 × 6 + 11 × 6 → Distributive Law
*Explanation:* `18×6 = (7+11)×6 = 7×6 + 11×6`.

16. (12 - 8) × 10 = 12×10 - 8×10 → Distributive Law
*Explanation:* Distributing multiplication over subtraction: `a×(b - c) = a×b - a×c`.

17. 11 × (4 × 3) = (11 × 4) × 3 → Associative Law (Multiplication)
*Explanation:* Regrouping multiplication.

18. 6 × 7 + 5 × 7 = (6 + 5) × 7 → Distributive Law
*Explanation:* Factoring out 7.

19. 10 × 9 = 9 × 10 → Commutative Law (Multiplication)
*Explanation:* Order doesn’t matter in multiplication.

20. 7 ÷ 3 = 3 ÷ 7 → ❗ Again, FALSE — not a law!
*Explanation:* `7÷3 ≈ 2.33`, `3÷7 ≈ 0.43` — not equal. Division is not commutative.

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📝 Final Answer Key:

| # | Expression | Law |
|---|----------------------------------------|----------------------------|
| 1 | 2 × 3 = 3 × 2 | Commutative (Mult) |
| 2 | (6+9)+8 = 6+(9+8) | Associative (Add) |
| 3 | 5 + 12 = 12 + 5 | Commutative (Add) |
| 4 | 6×8 + 4×8 = (6+4)×8 | Distributive |
| 5 | 5×11 + 12×11 = 17×11 | Distributive |
| 6 | (7×3)×9 = 7×(3×9) | Associative (Mult) |
| 7 | (3×5)×11 = 3×(5×11) | Associative (Mult) |
| 8 | (8×12)+9×12 = (8+9)×12 | Distributive |
| 9 | 4×2 = 2×4 | Commutative (Mult) |
|10 | 10×7 + 9×7 = (10+9)×7 | Distributive |
|11 | (11×4)×8 = 11×(4×8) | Associative (Mult) |
|12 | 6 ÷ 3 = 3 ÷ 6 | Not a valid law (False)|
|13 | 5×2 + 3×2 = 8×2 | Distributive |
|14 | 9 + (4+10) = (9+4)+10 | Associative (Add) |
|15 | 18×6 = 7×6 + 11×6 | Distributive |
|16 | (12-8)×10 = 12×10 - 8×10 | Distributive |
|17 | 11×(4×3) = (11×4)×3 | Associative (Mult) |
|18 | 6×7 + 5×7 = (6+5)×7 | Distributive |
|19 | 10×9 = 9×10 | Commutative (Mult) |
|20 | 7 ÷ 3 = 3 ÷ 7 | Not a valid law (False)|

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💡 Teacher’s Note:

Problems #12 and #20 are incorrect statements — they do not follow any algebraic law because division is not commutative. If this is for a student assignment, it might be intentional to test understanding — or an error in the worksheet.

✔ For correct answers, use the laws as shown above. For #12 and #20, you may write "None / False Statement" or "Division is not commutative".

Let me know if you’d like this formatted as a printable answer key!