| A | B |
|---|
| Commutative Property for Addition | a + b = b + a |
| Commutative Property for Multiplication | a x b = b x a |
| Associative Property for Addition | a + (b + c) = (a + b) + c |
| Associative Property for Multiplication | a x (b x c) = (a x b) x c |
| Distributive Property | a (b + c) = ab + ac |
| Additive Inverses | /n/ = /-n/ |
| Identity for Addition | n + (-n) = 0 |
| Identity for Multiplication | n/1 x 1/n = 1 (n cannot be 0) |
| Zero Property for Multiplication | n x 0 = 0 |
| Definition of Multiplication | 4 x n = n + n + n + n (repeated addition) |
| Definition of Division | a/b = a x 1/b (multiply by the reciprocal) |
| Definition of Subtraction | a - b = a + (-b) (add the inverse) |
| Substitution in Addition | If a = b, then a + n = b + n |
| Substitution in Multiplication | If a = b, then an = bn |
