| Term | Definition |
| Commutative Property of Multiplication | 3 x 2 = 2 x 3 |
| Commutative Property of Addition | 5 + 4 = 4 + 5 |
| Associative Property of Multiplication | (7 x 2) x 6 = 7 x (2 x 6) |
| Associative Property of Addition | (8 + 7) + 1 = 8 + (7 + 1) |
| Reflexive Property of Equality | 3 = 3 |
| Transative Property of Equality | If x = y and y = 3 then x = 3 |
| Symmetric Property of Equality | If 7 = a than a = 7 |
| Substitution Property | 3 - (4 + 5) = 3 - 9 |
| Identity Property of Addition | 3 + 0 = 3 |
| Definition of Subtraction | 3 - 7 = 3 + -7 |
| Identity Property of Multiplication | 5 x 1 = 5 |
| Multiplicative Property of Zero | 7 x 0 = 0 |
| Multiplicative Property of Negative 1 | 7 x -1 = -7 |
| Property of Reciprocals | 2 x 1/2 = 1 |
| Property of the Opposites | -(7 + 8) = -7 + -8 |