The most commonly known examples of commutativity are addition and multiplication of natural numbers; for example:

- 4 + 5 = 5 + 4 (since both expressions evaluate to 9)
- 2 × 3 = 3 × 2 (since both expressions evaluate to 6)

An Abelian group is a group whose operation is commutative.

A ring is called commutative if its multiplication is commutative, since the addition is commutative in any ring.

See also: Associativity, Distributive property