Using the Associative, Commutative and Distributive Properties for ... - Free Printable

Absolutely! Let’s solve this worksheet step by step, explaining how to use the Associative, Commutative, and Distributive Properties to simplify multiplication.

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## 📘 Section A: Using Associative & Commutative Properties

These properties let us reorder (commutative) or regroup (associative) numbers to make multiplication easier — usually by creating multiples of 10.

🔢 Example Given:

> `8 × 5 × 2 = 8 × (5 × 2) = 8 × 10 = 80`

We grouped 5 and 2 first because 5×2=10 → easy to multiply by 8.

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✔ Problem 1: `9 × 5 × 2`

- We can group 5 and 2 together: `(5 × 2) = 10`
- So: `9 × (5 × 2) = 9 × 10 = 90`

Answer:
```
9 × (5 × 2) = 9 × 10 = 90
```

---

✔ Problem 2: `5 × 7 × 2`

- Group 5 and 2: `(5 × 2) = 10`
- So: `(5 × 2) × 7 = 10 × 7 = 70`

Answer:
```
(5 × 2) × 7 = 10 × 7 = 70
```

*(Note: You could also write `5 × 2 × 7` — commutative property lets you reorder.)*

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✔ Problem 3: `2 × 12 × 5`

- Group 2 and 5: `(2 × 5) = 10`
- So: `(2 × 5) × 12 = 10 × 12 = 120`

Answer:
```
(2 × 5) × 12 = 10 × 12 = 120
```

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✔ Problem 4: `2 × 7 × 5 × 3`

- Group 2 and 5 → 10; group 7 and 3 → 21? But better to do 2×5=10, then 7×3=21 → 10×21=210
- Or: `(2 × 5) × (7 × 3) = 10 × 21 = 210`

Answer:
```
(2 × 5) × (7 × 3) = 10 × 21 = 210
```

*(You could also do `2 × 5 × 3 × 7` → 10 × 3 × 7 = 30 × 7 = 210 — same result.)*

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✔ Problem 5: `5 × 9 × 2 × 3`

- Group 5 and 2 → 10; group 9 and 3 → 27 → 10 × 27 = 270
- So: `(5 × 2) × (9 × 3) = 10 × 27 = 270`

Answer:
```
(5 × 2) × (9 × 3) = 10 × 27 = 270
```

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✔ Problem 6: `2 × 11 × 5 × 4`

- Group 2 and 5 → 10; group 4 and 11 → 44 → 10 × 44 = 440
- So: `(2 × 5) × (4 × 11) = 10 × 44 = 440`

Answer:
```
(2 × 5) × (4 × 11) = 10 × 44 = 440
```

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✔ Problem 7: `8 × 5 × 2 × 7`

- Group 5 and 2 → 10; so: `8 × 10 × 7 = 80 × 7 = 560`
- Or: `(5 × 2) × (8 × 7) = 10 × 56 = 560`

Answer:
```
(5 × 2) × (8 × 7) = 10 × 56 = 560
```

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## 📘 Section B: Using Distributive Property

This property breaks down a number into parts (usually tens + ones) to multiply more easily.

> `a × (b + c) = a×b + a×c`

Example given:
> `3 × 14 = 3 × (10 + 4) = 3×10 + 3×4 = 30 + 12 = 42`

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✔ Problem 1: `4 × 19`

Break 19 into 10 + 9

```
4 × 19 = 4 × (10 + 9)
= 4 × 10 + 4 × 9
= 40 + 36
= 76
```

Answer:
```
4 × (10 + 9)
= 4 × 10 + 4 × 9
= 40 + 36
= 76
```

---

✔ Problem 2: `5 × 18`

Break 18 into 10 + 8

```
5 × 18 = 5 × (10 + 8)
= 5 × 10 + 5 × 8
= 50 + 40
= 90
```

Answer:
```
5 × (10 + 8)
= 5 × 10 + 5 × 8
= 50 + 40
= 90
```

---

✔ Problem 3: `7 × 14`

Break 14 into 10 + 4

```
7 × 14 = 7 × (10 + 4)
= 7 × 10 + 7 × 4
= 70 + 28
= 98
```

Answer:
```
7 × (10 + 4)
= 7 × 10 + 7 × 4
= 70 + 28
= 98
```

---

✔ Problem 4: `6 × 15`

Break 15 into 10 + 5

```
6 × 15 = 6 × (10 + 5)
= 6 × 10 + 6 × 5
= 60 + 30
= 90
```

Answer:
```
6 × (10 + 5)
= 6 × 10 + 6 × 5
= 60 + 30
= 90
```

---

✔ Problem 5: `8 × 16`

Break 16 into 10 + 6

```
8 × 16 = 8 × (10 + 6)
= 8 × 10 + 8 × 6
= 80 + 48
= 128
```

Answer:
```
8 × (10 + 6)
= 8 × 10 + 8 × 6
= 80 + 48
= 128
```

---

✔ Problem 6: `3 × 24`

Break 24 into 20 + 4

```
3 × 24 = 3 × (20 + 4)
= 3 × 20 + 3 × 4
= 60 + 12
= 72
```

Answer:
```
3 × (20 + 4)
= 3 × 20 + 3 × 4
= 60 + 12
= 72
```

---

✔ Problem 7: `4 × 23`

Break 23 into 20 + 3

```
4 × 23 = 4 × (20 + 3)
= 4 × 20 + 4 × 3
= 80 + 12
= 92
```

Answer:
```
4 × (20 + 3)
= 4 × 20 + 4 × 3
= 80 + 12
= 92
```

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## ✔ Final Answers Summary:

Section A:

1) `9 × (5 × 2) = 9 × 10 = 90`
2) `(5 × 2) × 7 = 10 × 7 = 70`
3) `(2 × 5) × 12 = 10 × 12 = 120`
4) `(2 × 5) × (7 × 3) = 10 × 21 = 210`
5) `(5 × 2) × (9 × 3) = 10 × 27 = 270`
6) `(2 × 5) × (4 × 11) = 10 × 44 = 440`
7) `(5 × 2) × (8 × 7) = 10 × 56 = 560`

Section B:

1) `4 × (10 + 9) = 40 + 36 = 76`
2) `5 × (10 + 8) = 50 + 40 = 90`
3) `7 × (10 + 4) = 70 + 28 = 98`
4) `6 × (10 + 5) = 60 + 30 = 90`
5) `8 × (10 + 6) = 80 + 48 = 128`
6) `3 × (20 + 4) = 60 + 12 = 72`
7) `4 × (20 + 3) = 80 + 12 = 92`

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✔ You’ve now mastered using these three key properties to simplify multiplication!
These strategies are super helpful for mental math and building number sense.

Let me know if you’d like a printable version or want to check your own answers! 😊