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

Absolutely! Let’s solve this worksheet step by step, identifying which property of multiplication is shown and then filling in the missing numbers using those properties.

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## 🔹 PART 1: Identify the Property

1. `4 × 6 = (4 × 5) + (4 × 1)`

This shows breaking down 6 into 5 + 1, then multiplying 4 by each part and adding.
✔ Distributive Property:
> `a × (b + c) = (a × b) + (a × c)`

Here, `4 × (5 + 1) = (4 × 5) + (4 × 1)`

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2. `5 × 7 = 7 × 5`

The order of the numbers is switched, but the product stays the same.
✔ Commutative Property:
> `a × b = b × a`

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3. `4 × (2 × 5) = (4 × 2) × 5`

The grouping of numbers changes — parentheses move — but the product is unchanged.
✔ Associative Property:
> `(a × b) × c = a × (b × c)`

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## ✔ Answers for Part 1:
- `4 × 6 = (4 × 5) + (4 × 1)` → Distributive Property
- `5 × 7 = 7 × 5` → Commutative Property
- `4 × (2 × 5) = (4 × 2) × 5` → Associative Property

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

We’ll apply the same three properties to find the missing numbers.

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Row 1:

Left: `6 × 8 = (6 × 4) + (6 × __)`
→ This is Distributive Property. We broke 8 into 4 + ? → 8 - 4 = 4

✔ Answer: 4

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

✔ Answer: 3

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Row 2:

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

✔ Answer: 2

Right: `4 × (2 × 6) = (__ × 2) × 6`
→ Associative Property: Grouping changed → 4 stays with 2

✔ Answer: 4

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Row 3:

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

✔ Answer: 4

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

✔ Answer: 9

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Row 4:

Left: `2 × (6 × 5) = (__ × 6) × 5`
→ Associative Property: Move parentheses → 2

✔ Answer: 2

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

✔ Answer: 4

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Row 5:

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

✔ Answer: 6

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

✔ Answer: 3

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## ✔ FINAL ANSWERS:

Part 1: Properties

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

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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✔ All done! You’ve now correctly identified the properties and used them to fill in the blanks. Great job practicing multiplication properties!