### Commutative, Associative and Distributive Laws

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Commutative Laws

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

### 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) …

### (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 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