Properties of Multiplication - Math Worksheets - Free Printable

The image you've uploaded is a completed "Properties of Multiplication" worksheet titled "Identify The Property", and it includes an answer key. The task was to identify the correct multiplication property used in each equation.

Let's go through each equation, explain the property used, and verify the answers provided in the answer key.

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🔹 1. $ 2 \times (4 + 3) = (2 \times 4) + (2 \times 3) $

- Property: Distributive
- ✔ Correct
- 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.
- $ 2 \times (4+3) = 2 \times 7 = 14 $
- $ (2 \times 4) + (2 \times 3) = 8 + 6 = 14 $

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🔹 2. $ 6 \times 1 = 6 $

- Property: Identity
- ✔ Correct
- Explanation: The identity property of multiplication states that any number multiplied by 1 remains unchanged.

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🔹 3. $ 4 \times 0 = 0 $

- Property: Zero
- ✔ Correct
- Explanation: The zero property of multiplication states that any number multiplied by zero equals zero.

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🔹 4. $ 5 \times 8 = 8 \times 5 $

- Property: Commutative
- ✔ Correct
- Explanation: The commutative property states that changing the order of factors does not change the product.

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🔹 5. $ 7 \times (3 - 2) = (7 \times 3) - (7 \times 2) $

- Property: Distributive
- ✔ Correct
- Explanation: This is the distributive property applied to subtraction. It shows that multiplication distributes over subtraction:
- $ 7 \times (3 - 2) = 7 \times 1 = 7 $
- $ (7 \times 3) - (7 \times 2) = 21 - 14 = 7 $

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🔹 6. $ 3 \times (8 \times 4) = (3 \times 8) \times 4 $

- Property: Associative
- ✔ Correct
- Explanation: The associative property states that the way numbers are grouped does not affect the product when multiplying three or more numbers.

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🔹 7. $ 6 \times 5 = 5 \times 6 $

- Property: Commutative
- ✔ Correct
- Explanation: Again, this shows that changing the order of the factors doesn’t change the product.

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🔹 8. $ 12 \times 0 = 0 $

- Property: Zero
- ✔ Correct
- Explanation: Any number times zero is zero.

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🔹 9. $ 9 \times (5 \times 2) = (9 \times 5) \times 2 $

- Property: Associative
- ✔ Correct
- Explanation: Grouping changes, but the result stays the same:
- Left: $ 9 \times (5 \times 2) = 9 \times 10 = 90 $
- Right: $ (9 \times 5) \times 2 = 45 \times 2 = 90 $

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🔹 10. $ 4 \times (6 + 7) = (4 \times 6) + (4 \times 7) $

- Property: Distributive
- ✔ Correct
- Explanation: Distributive property again — multiply 4 across the sum:
- $ 4 \times (6+7) = 4 \times 13 = 52 $
- $ (4 \times 6) + (4 \times 7) = 24 + 28 = 52 $

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🔹 11. $ 13 \times 1 = 13 $

- Property: Identity
- ✔ Correct
- Explanation: Any number times 1 is itself.

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🔹 12. $ 9 \times 5 = 5 \times 9 $

- Property: Commutative
- ✔ Correct
- Explanation: Order of multiplication doesn't matter.

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✔ Final Assessment:

All answers in the answer key are correct. The properties identified match perfectly with the equations:

| Equation | Property |
|--------|----------|
| $ 2(4+3) = (2×4)+(2×3) $ | Distributive |
| $ 6×1=6 $ | Identity |
| $ 4×0=0 $ | Zero |
| $ 5×8=8×5 $ | Commutative |
| $ 7(3−2)=(7×3)−(7×2) $ | Distributive |
| $ 3(8×4)=(3×8)×4 $ | Associative |
| $ 6×5=5×6 $ | Commutative |
| $ 12×0=0 $ | Zero |
| $ 9(5×2)=(9×5)×2 $ | Associative |
| $ 4(6+7)=(4×6)+(4×7) $ | Distributive |
| $ 13×1=13 $ | Identity |
| $ 9×5=5×9 $ | Commutative |

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📌 Summary of Properties:

- Distributive: $ a(b + c) = ab + ac $
- Commutative: $ a × b = b × a $
- Associative: $ (a × b) × c = a × (b × c) $
- Identity: $ a × 1 = a $
- Zero: $ a × 0 = 0 $

✔ All problems are correctly solved and labeled.

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