Distributive property rule in multiplication No.1 | Worksheets ... - Free Printable

You're working on a worksheet titled “Distributive Property Rule in Multiplication — No. 1”. The goal is to apply the distributive property of multiplication over addition, which states:

> a × (b + c) = a × b + a × c

In this worksheet, you’re breaking down a two-digit number (like 11, 13, etc.) into 10 + some digit, then multiplying each part by 5, and adding the results.

Let’s solve each problem step-by-step:

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1. `11 × 5 = 10 × 5 + ___ × 5 = ___`

- Break 11 into 10 + 1
- So: `11 × 5 = (10 + 1) × 5 = 10×5 + 1×5`
- Fill in: 1 and then compute: `50 + 5 = 55`

✔ Answer:
11 × 5 = 10 × 5 + _1_ × 5 = _55_

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2. `13 × 5 = 10 × 5 + ___ × 5 = ___`

- 13 = 10 + 3 → `(10 + 3) × 5 = 10×5 + 3×5`
- Fill in: 3, then `50 + 15 = 65`

✔ Answer:
13 × 5 = 10 × 5 + _3_ × 5 = _65_

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3. `15 × 5 = 10 × 5 + ___ × 5 = ___`

- 15 = 10 + 5 → `10×5 + 5×5 = 50 + 25 = 75`

✔ Answer:
15 × 5 = 10 × 5 + _5_ × 5 = _75_

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4. `___ × 5 = ___ × 5 + 8 × 5 = ___`

- Here, we see “+ 8 × 5”, so the second part is 8.
- Since it’s broken into “__ × 5 + 8 × 5”, and the first part is likely 10 × 5 (as in all others), then total = 10 + 8 = 18
- So: `18 × 5 = 10 × 5 + 8 × 5 = 50 + 40 = 90`

✔ Answer:
_18_ × 5 = _10_ × 5 + 8 × 5 = _90_

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5. `19 × 5 = ___ × 5 + ___ × 5 = ___`

- 19 = 10 + 9 → `10×5 + 9×5 = 50 + 45 = 95`

✔ Answer:
19 × 5 = _10_ × 5 + _9_ × 5 = _95_

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6. `12 × 5 = 10 × 5 + ___ × 5 = ___`

- 12 = 10 + 2 → `50 + 10 = 60`

✔ Answer:
12 × 5 = 10 × 5 + _2_ × 5 = _60_

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7. `14 × 5 = 10 × 5 + ___ × 5 = ___`

- 14 = 10 + 4 → `50 + 20 = 70`

✔ Answer:
14 × 5 = 10 × 5 + _4_ × 5 = _70_

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8. `16 × 5 = 10 × 5 + ___ × 5 = ___`

- 16 = 10 + 6 → `50 + 30 = 80`

✔ Answer:
16 × 5 = 10 × 5 + _6_ × 5 = _80_

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9. `18 × 5 = ___ × 5 + 8 × 5 = ___`

- Same as problem #4 — 18 = 10 + 8 → `10×5 + 8×5 = 50 + 40 = 90`

✔ Answer:
18 × 5 = _10_ × 5 + 8 × 5 = _90_

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10. `20 × 5 = ___ × 5 + ___ × 5 = ___`

- 20 = 10 + 10 → `10×5 + 10×5 = 50 + 50 = 100`

✔ Answer:
20 × 5 = _10_ × 5 + _10_ × 5 = _100_

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## ✔ Final Completed Worksheet:

```
11 × 5 = 10 × 5 + 1 × 5 = 55
13 × 5 = 10 × 5 + 3 × 5 = 65
15 × 5 = 10 × 5 + 5 × 5 = 75
18 × 5 = 10 × 5 + 8 × 5 = 90
19 × 5 = 10 × 5 + 9 × 5 = 95
12 × 5 = 10 × 5 + 2 × 5 = 60
14 × 5 = 10 × 5 + 4 × 5 = 70
16 × 5 = 10 × 5 + 6 × 5 = 80
18 × 5 = 10 × 5 + 8 × 5 = 90
20 × 5 = 10 × 5 + 10 × 5 = 100
```

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## 🧠 Why This Works (The Math Behind It):

This exercise teaches you how to use the distributive property to simplify multiplication. Instead of multiplying 17 × 5 directly, you break 17 into 10 + 7, multiply each by 5, then add:

> 17 × 5 = (10 + 7) × 5 = 10×5 + 7×5 = 50 + 35 = 85

This is especially helpful for mental math or when learning multiplication facts!

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Let me know if you want to try more problems like this or need a printable version! 😊