Mathematics Glossary » Table 3 #
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 |