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Arithmetic Properties: Associative, Commutative & Distributive Explained

Associative Property

In both addition and multiplication, the grouping of terms does not affect the result. This allows us to freely place parentheses wherever convenient:

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

Commutative Property

Terms in addition or multiplication can be reordered without changing the outcome:

a + b = b + a            ab = ba

Distributive Property

When a term multiplies a sum, the multiplication distributes over each addend:

a(b + c) = ab + ac

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