Distributive Property Math Worksheet - Matching Multiplication Expressions

Let's solve this step-by-step.

We are asked to match each multiplication expression (like 8 × 9, 7 × 11, etc.) with its equivalent expression using the distributive property, which is:

> a × b = a × (c + d) = (a × c) + (a × d)

So we need to break down each multiplication into two parts that add up to the original number, then apply the distributive property.

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Step 1: Understand the format

Each problem like "8 × 9" needs to be rewritten as something like:
> (8 × 4) + (8 × 5) → because 4 + 5 = 9

Then match it to the correct option in the grid below.

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Let's go through each one:

#### 1. 8 × 9
Break 9 into 4 + 5 → (8 × 4) + (8 × 5)
→ This matches (B): (8×4) + (8×5)

✔ Match: 1 → B

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#### 2. 7 × 11
Break 11 into 7 + 4 → (7 × 7) + (7 × 4)
→ This matches (C): (7×7) + (7×4)

✔ Match: 2 → C

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#### 3. 3 × 8
Break 8 into 5 + 3 → (3 × 5) + (3 × 3)
→ This matches (G): (3×5) + (3×3)

✔ Match: 3 → G

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#### 4. 4 × 9
Break 9 into 6 + 3 → (4 × 6) + (4 × 3)
→ This matches (D): (4×6) + (4×3)

✔ Match: 4 → D

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#### 5. 8 × 8
Break 8 into 5 + 3 → (8 × 5) + (8 × 3)
→ This matches (F): (8×5) + (8×3)

✔ Match: 5 → F

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#### 6. 5 × 15
Break 15 into 10 + 5 → (5 × 10) + (5 × 5)
→ This matches (E): (5×10) + (5×5)

✔ Match: 6 → E

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#### 7. 6 × 9
Break 9 into 5 + 4 → (6 × 5) + (6 × 4)
→ This matches (A): (6×5) + (6×4)

✔ Match: 7 → A

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#### 8. 3 × 12
Break 12 into 6 + 6 → (3 × 6) + (3 × 6)
→ This matches (H): (3×6) + (3×6)

✔ Match: 8 → H

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#### 9. 4 × 7
Break 7 into 3 + 4 → (4 × 3) + (4 × 4)
→ This matches (I): (4×3) + (4×4)

✔ Match: 9 → I

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#### 10. 9 × 9
Break 9 into 5 + 4 → (9 × 5) + (9 × 4)
→ This matches (J): (9×5) + (9×4)

✔ Match: 10 → J

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#### 11. 7 × 6
Break 6 into 4 + 2 → (7 × 4) + (7 × 2)
→ This matches (K): (7×4) + (7×2)

✔ Match: 11 → K

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Final Answer Key:

| Problem | Match |
|--------|-------|
| 1. 8 × 9 | B |
| 2. 7 × 11 | C |
| 3. 3 × 8 | G |
| 4. 4 × 9 | D |
| 5. 8 × 8 | F |
| 6. 5 × 15 | E |
| 7. 6 × 9 | A |
| 8. 3 × 12 | H |
| 9. 4 × 7 | I |
| 10. 9 × 9 | J |
| 11. 7 × 6 | K |

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Explanation of Distributive Property:

The distributive property says:
> a × (b + c) = (a × b) + (a × c)

We used this by splitting the second number into two addends, then distributing the first number over the sum.

For example:
- 8 × 9 = 8 × (4 + 5) = (8 × 4) + (8 × 5) = 32 + 40 = 72 ✔

This helps students understand multiplication as repeated addition and builds number sense.

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✔ Objective Met: 3.OA.5 – Apply properties of operations as strategies to multiply and divide.

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