|
 commutative property of addition | a + b = b + a |
| associative property of addition | a + (b + c) = (a + b) + c |
| commutative property of multiplication | ab = ba |
| associative property of multiplication | a(bc) = (ab)c |
| distributive property | a(b + c) = ab + ac |
| additive identity | a + 0 = a |
| multiplicative identity | a • 1 = a |
| additive inverse | a + -a = 0 |
| multiplicative inverse | a • 1/a = 1 |
| zero product property | a • 0 = 0 |
| reflexive property | a = a |
| symmetric property | If a = b, then b = a. |
| transitive property | If a = b and b =c, then a = c. |
| substitution property | If a = b, then we can replace a with b in any expression. |
| zero product property | If ab = 0, then a = 0 or b = 0. |
| addition property of equality | If A = B, then A + c = B + c. |
| subtraction property of equality | If A = B, then A - c = B - c. |
| multiplication property of equality | If A = B, then A • c = B • c. |
| division property of equality | If A = B and c ≠ 0, then A ÷ c = B ÷ c. |
| addition property of inequality | If A > B, then A + c > B + c. |
| subtraction property of inequality | If A > B, then A - c > B - c. |
| multiplication property of inequality | If A > B and c > 0, then A • c > B • c, but if c < 0, then A • c < B • c. |
| division property of inequality | If A > B and c > 0, then A ÷ c > B ÷ c, but if c < 0, then A ÷ c < B ÷ c. |
| commutative property of addition | (3 + -5) + 2 = (-5 + 3) + 2 |
| associative property of addition | (3 + -5) + 2 = 3 + (-5 + 2) |
| commutative property of multiplication | 3 • (-5 • 2) = 3 • (2 • -5) |
| associative property of multiplication | 3 • (-5 • 2) = (3 • -5) • 2 |
| distributive property | -8(2x - 3) = -16x + 24 |
| additive identity | 0 + -9 = -9 |
| multiplicative identity | 1 • -5 = -5 |
| additive inverse | -2 + 2 = 0 |
| multiplicative inverse | ¼ • 4 = 1 |
| reflexive property | XY = XY |
| symmetric property | If 3 = x, then x = 3. |
| transitive property | If x = y and y = 4, then x = 4. |
| multiplication property of zero | 0 • -¾ = 0 |
| addition property of equality | If 2x - 7 = 5, then 2x = 12. |
| subtraction property of equality | If 16 = 3x + 4, then 12 = 3x. |
| multiplication property of equality | If ½x = 5.5, then x = 11. |
| division property of equality | If 4x = 24, then x = 6. |
| addition property of inequality | If x - 1 ≤ 3, then x ≤ 4. |
| subtraction property of inequality | If x + 2 ≥ 1, then x ≥ -1. |
| multiplication property of inequality | If -¼x ≤ 5, then x ≥ -20. |
| division property of inequality | If -3x ≥ -9, then x ≤ 3. |