Properties of Multiplication worksheet for identifying commutative, associative, and distributive properties.

Absolutely! Let’s solve this worksheet step by step. The worksheet is about Properties of Multiplication: Commutative, Associative, and Distributive.

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## 🧩 PART 1: Identify the Property Shown

1. `4 × 6 = (4 × 5) + (4 × 1)`

- Notice that 6 is broken into 5 + 1.
- Then 4 is multiplied by each part separately and added.
- This matches the Distributive Property:
> a × (b + c) = (a × b) + (a × c)

✔ Answer: Distributive Property

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2. `5 × 7 = 7 × 5`

- The order of the numbers is switched.
- This matches the Commutative Property:
> a × b = b × a

✔ Answer: Commutative Property

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3. `4 × (2 × 5) = (4 × 2) × 5`

- The grouping of numbers changes — parentheses move.
- This matches the Associative Property:
> a × (b × c) = (a × b) × c

✔ Answer: Associative Property

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## 🔢 PART 2: Use Properties to Fill in Missing Numbers

We’ll use the same properties to find the missing values.

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Row 1:

Left: `6 × 8 = (6 × 4) + (6 × __)`
→ This is the Distributive Property.
8 = 4 + 4 → So the missing number is 4

✔ Answer: 4

Right: `3 × 7 = 7 × __`
→ Commutative Property → 3 × 7 = 7 × 3

✔ Answer: 3

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Row 2:

Left: `9 × 2 = __ × 9`
→ Commutative Property → 9 × 2 = 2 × 9

✔ Answer: 2

Right: `4 × (2 × 6) = (__ × 2) × 6`
→ Associative Property → Grouping changes, so 4 stays with 2
So: `(4 × 2) × 6`

✔ Answer: 4

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Row 3:

Left: `3 × (5 × 4) = (3 × 5) × __`
→ Associative Property → Move parentheses: 3×(5×4) = (3×5)×4

✔ Answer: 4

Right: `9 × 7 = (9 × 5) + (__ × 2)`
→ Distributive Property → 7 = 5 + 2 → So we need 9 × 2
So: `(9 × 5) + (9 × 2)`

✔ Answer: 9

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Row 4:

Left: `2 × (6 × 5) = (__ × 6) × 5`
→ Associative Property → 2 should stay with 6 → (2 × 6) × 5

✔ Answer: 2

Right: `3 × 9 = (3 × 5) + (3 × __)`
→ Distributive Property → 9 = 5 + 4 → So 3 × 4

✔ Answer: 4

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Row 5:

Left: `6 × 3 = 3 × __`
→ Commutative Property → 6 × 3 = 3 × 6

✔ Answer: 6

Right: `3 × 8 = (3 × 5) + (3 × __)`
→ Distributive Property → 8 = 5 + 3 → So 3 × 3

✔ Answer: 3

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## ✔ FINAL ANSWERS:

Part 1: Properties

1. Distributive Property
2. Commutative Property
3. Associative Property

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Part 2: Missing Numbers (Left to Right, Top to Bottom)

| Left Column | Right Column |
|-------------|--------------|
| 4 | 3 |
| 2 | 4 |
| 4 | 9 |
| 2 | 4 |
| 6 | 3 |

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You’re all set! These properties are foundational for understanding algebra and simplifying expressions later on. Great job practicing them! 🎉