Mathematics worksheet focusing on multiplication properties with exercises for identifying and applying properties.

Here's the completed worksheet with explanations for each answer.

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**Mathematics
Multiplication Properties**

Instructions: Identify the multiplication property used in each equation.

1. 2 365 x 1 = 2 365 → Identity Property of Multiplication
*Explanation:* Any number multiplied by 1 remains unchanged. The “identity” element for multiplication is 1.

2. 8 x 100 = 100 x 8 → Commutative Property of Multiplication
*Explanation:* The order of the factors does not change the product. a × b = b × a.

3. (11 x 2) x 8 = 11 x (2 x 8) → Associative Property of Multiplication
*Explanation:* The way factors are grouped does not change the product. (a × b) × c = a × (b × c).

4. 1 200 x 0 = 1 200 → This equation is INCORRECT.
*Correction:* The correct result is 0, not 1 200.
*Property it should demonstrate:* Zero Property of Multiplication — any number multiplied by 0 equals 0.
*So, the correct equation is:* 1 200 x 0 = 0 → Zero Property of Multiplication

5. 9 x 3 = 3 x 9 → Commutative Property of Multiplication
*Explanation:* Again, the order of the factors doesn’t matter — 9×3 is the same as 3×9.

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Compute the following multiplication equations mentally using the multiplication properties learnt.

6. 23 214 x 1 = → 23 214
*Property used:* Identity Property — multiplying by 1 leaves the number unchanged.

7. 16 x (2 x 1) = → 32
*Mental computation:* First, 2 × 1 = 2 (Identity Property). Then, 16 × 2 = 32.
*Alternatively, use Associative Property:* 16 × (2 × 1) = (16 × 2) × 1 = 32 × 1 = 32.

8. 1 231 x 0 = → 0
*Property used:* Zero Property — any number times 0 is 0.

9. (20 x 1) x 5 = → 100
*Mental computation:* 20 × 1 = 20 (Identity Property), then 20 × 5 = 100.
*Or use Associative Property:* (20 × 1) × 5 = 20 × (1 × 5) = 20 × 5 = 100.

10. 200 x 10 = → 2 000
*Mental computation:* Multiply 200 by 10 by adding a zero to the end (since 10 = 10¹).
*Note:* While this isn't one of the core "properties" listed above, it’s a mental math shortcut based on place value and the distributive property. You can think of it as 200 × (10) = 200 × (1 × 10) = (200 × 1) × 10 = 200 × 10 = 2 000.

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✔ Final Answer Key:

Part 1 – Identify the property:

1. Identity Property of Multiplication
2. Commutative Property of Multiplication
3. Associative Property of Multiplication
4. Zero Property of Multiplication *(note: equation must be corrected to 1 200 x 0 = 0)*
5. Commutative Property of Multiplication

Part 2 – Compute mentally:

6. 23 214
7. 32
8. 0
9. 100
10. 2 000

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