| Additive Identity | a + 0 = a | |
| Additive Inverse | a + (-a) = 0 | |
| Associative of Addition | (a + b) + c = a + (b + c) | |
| Commutative of Addition | a + b = b + a | |
| Definition of Subtraction | a - b = a + (-b) | |
| Multiplicative Identity | a * 1 = a | |
| (Multiplication times 0) | a * 0 = 0 | |
| Associative of Multiplication | (a * b) * c = a * (b * c) | |
| Commutative of Multiplication | a * b = b * a | |
| Distributive Law | a(b + c) = ab + ac | |
| Definition of Division | a / b = a(1/b) | |