Mathematics Glossary » Table 3

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The properties of operations. Here a, b and c stand for arbitrary numbers in a given number system. The properties of operations apply to the rational number system, the real number system, and the complex number.

Associative property of addition (a +b) + c = a + (b+c)
Commutative property of addition a + b = b + a
Additive identity property of 0 a + 0 = 0 + a = a
Existence of additive inverses For every a there exists -a so that a + (-a) = (-a) + a = 0
Associative property of multiplication (a x b) x c = a x (b x c)
Commutative property of multplication a x b = b x a
Multiplicative identity property 1 a x 1 = 1 x a = a
Existence of multiplicative inverses For every a ≠ 0 there exists 1/a so that a x 1/a = 1/a x a = 1
Distributive propery of multiplication over additions a x (b + c) = a x b + a x c