| A | B |
|---|
| Reflexive Property | For every number a, a = a. |
| Symmetric Property | For all numbers a & b, if a = b, then b = a. |
| Transitive Property | For all numbers a, b & c, if a = b & b = c, then a = c. (Ex: If BC = XY and XY = AD, then BC = AD --a bit like the Law of Syllogism) |
| Addition/Subtraction Property | For all numbers a, b, & c, if a = b, then a + c = b + c and a - c = b - c. |
| Multiplication/Division Property | For all numbers a, b, and c, if a = b, then a * c = b * c, and if c not equal to zero, a ÷ c = b ÷ c. |
| Substitution Property | For all numbers a & b, if a = b, then a may be replaced by b in any equation or expression. (Ex: If BC = XY and AD = XY, then BC = AD) |
| Distributive Property | For all numbers a, b, & c, a(b + c) = ab + ac. |
| Additive Inverse Property | a + (-a) = 0 |
| Multiplicative Inverse Property | a * (1/a) = 1 |
| Additive Identity Property | a + 0 = a |
| Multiplicative Identity Property | a * 1 = a |
| Multiplication Property of Zero | a * 0 = 0 |
| Associative Property of Addition | a + b = b + a |
| Commutative Property of Addition | a + (b + c) = (a + b) + c |
| Associative Property of Multiplication | a * b = b * a |
| Commutative Property of Multiplication | a * (b * c) = (a * b) * c |
