### Commutative, Associative and Distributive Laws

**Commutative Laws**

The “Commutative Laws” say you can **swap numbers** over and still get the same answer …

**… when you add:**

**a + b = b + a**

**… or when you multiply:**

**a × b = b × a**

**Associative Laws**

The “Associative Laws” say that it doesn’t matter how you group the numbers (i.e. which you calculate first) …

**… when you add:**

**(a + b) + c = a + (b + c)**

**… or when you multiply:**

**(a × b) × c = a × (b × c)**

**Distributive Law**

The “Distributive Law” is the BEST one of all, but needs careful attention.

This is what it lets you do:

3 lots of **(2+4)** is the same as **3 lots of 2** plus **3 lots of 4**

So, the **3×** can be “distributed” across the **2+4**, into **3×2** and **3×4**

Try the calculations yourself:

- 3 × (
**2 + 4**) = 3 ×**6**= 18 - 3×2 + 3×4 = 6 + 12 = 18

Either way gets the same answer.

**But Don’t go too far!**

These laws are to do with adding or multiplying, not dividing or subtracting.

The Commutative Law does **not** work for division:

Example: 12 / 3 = **4**, but 3 / 12 = **¼**

The Associative Law does **not** work for subtraction:

Example: (9 – 4) – 3 = 5 – 3 = **2**, but 9 – (4 – 3) = 9 – 1 = **8**

The Distributive Law does **not** work for division:

Example: 24 / (4 + 8 ) = 24 / 12 = **2**, but 24 / 4 + 24 / 8 = 6 + 3 = **9**