The Distributive Property of Multiplication (3rd Grade) online ... - Free Printable

This worksheet is designed to teach the distributive property of multiplication — specifically, breaking down a multiplication problem like `6 × 4` into `(5 × 4) + (1 × 4)` to make it easier to solve using known facts (like multiplying by 5).

Let’s solve each part step-by-step.

---

Part a: 6 × 4

We’re shown an array of 6 rows and 4 columns. It’s broken into two parts:
- Top 5 rows: `(5 × 4) = 20` ← already filled
- Bottom 1 row: `(1 × 4) = ___`

→ `1 × 4 = 4`

Now fill in the equation:

```
(6 × 4) = (5 × 4) + (1 × 4)
= 20 + ___
= ___
```

→ `20 + 4 = 24`

✔ Final answers for part a:
- `6 × 4 = 24`
- `(1 × 4) = 4`
- `= 20 + 4`
- `= 24`

---

Part b: 7 × 4

Array: 7 rows × 4 columns → broken into 5 rows + 2 rows

- `(5 × 4) = ___` → `5 × 4 = 20`
- `(2 × 4) = ___` → `2 × 4 = 8`

Equation:

```
(7 × 4) = (5 × 4) + (2 × 4)
= ___ + ___
= 28 ← given
```

→ `20 + 8 = 28` ✓

✔ Final answers for part b:
- `7 × 4 = 28`
- `(5 × 4) = 20`
- `(2 × 4) = 8`
- `= 20 + 8`
- `= 28`

---

Part c: 8 × 4

Array: 8 rows × 4 columns → broken into 5 rows + 3 rows

- `(5 × 4) = ___` → `5 × 4 = 20`
- `( __ × 4) = ___` → since 8 - 5 = 3, so `(3 × 4) = 12`

Equation:

```
(8 × 4) = (5 × 4) + ( __ × 4)
= ___ + ___
= ___
```

→ `20 + 12 = 32`

✔ Final answers for part c:
- `8 × 4 = 32`
- `(5 × 4) = 20`
- `(3 × 4) = 12`
- `= 20 + 12`
- `= 32`

---

Part d: 9 × 4

Array: 9 rows × 4 columns → broken into 5 rows + 4 rows

- `(5 × 4) = ___` → `5 × 4 = 20`
- `( __ × 4) = ___` → since 9 - 5 = 4, so `(4 × 4) = 16`

Equation:

```
(9 × 4) = (5 × 4) + ( __ × 4)
= ___ + ___
= ___
```

→ `20 + 16 = 36`

✔ Final answers for part d:
- `9 × 4 = 36`
- `(5 × 4) = 20`
- `(4 × 4) = 16`
- `= 20 + 16`
- `= 36`

---

## ✔ Final Completed Answers:

a.

- `6 × 4 = 24`
- `(1 × 4) = 4`
- `= 20 + 4`
- `= 24`

b.

- `7 × 4 = 28`
- `(5 × 4) = 20`
- `(2 × 4) = 8`
- `= 20 + 8`
- `= 28`

c.

- `8 × 4 = 32`
- `(5 × 4) = 20`
- `(3 × 4) = 12`
- `= 20 + 12`
- `= 32`

d.

- `9 × 4 = 36`
- `(5 × 4) = 20`
- `(4 × 4) = 16`
- `= 20 + 16`
- `= 36`

---

## 💡 Key Concept: Distributive Property

You’re learning that:
> `a × b = (c × b) + ((a - c) × b)`

Here, we always split the first number (`a`) into `5 + (a-5)`, because `5 × 4` is easy to remember (it’s half of 10×4). This strategy helps you solve harder multiplication facts using easier ones.

Great job practicing this foundational math skill! 🎯