Commutative Laws
The commutative laws state that the order in which you add or multiply two real numbers does not affect the result.

The Commutative Law of Addition: a + b = b + a

The Commutative Law of Multiplication: ab = ba


The Associative Laws

The associative laws state the when you add or multiply any three real numbers, the grouping (or association) of the numbers does not affect the result.

The Associative Law of Addition: (a + b) + c = a + (b + c)

The Associative Law of Multiplication: (ab)c = a(bc)


The Distributive Law

Multiplication is distributive over addition: for any numbers a, b and c

a(b + c) = (ab + ac)

and

(b + c)a = (ba + ca)

The distributive law allows us to 'multiply out brackets'.