Key idea: Properties of whole-number addition and multiplication
**Commutative**: a + b = b + a, and a × b = b × a. Order does not matter for addition or multiplication.
**Associative**: (a + b) + c = a + (b + c), and (a × b) × c = a × (b × c). Grouping does not matter.
**Distributive**: a × (b + c) = a × b + a × c. Multiplication 'distributes over' addition. This is one of the most useful rules in all of maths.
**Identity**: a + 0 = a (zero is the additive identity), and a × 1 = a (one is the multiplicative identity).
**Multiplying by zero**: a × 0 = 0 for every whole number a.