Question | Answer |
Addition Property of Equality | For every real number a, b, and c, if a = b, then a + c = b + c. |
Subtraction Property of Equality | For every real number a, b, and c, if a = b, then a - c = b - c. |
Multiplication Property of Equality | For every real number a, b, and c, if a = b, then a * c = b * c. |
Division Property of Equality | For every real number a, b, and c, where c is nonzero, if a = b, then a/c = b/c. |
Identity Property of Addition | For every real number a, a + 0 = a. |
Inverse Property of Addition | For every real number a, there is an additive inverse -a such that a + (-a) = 0. |
Identity Property of Multiplication | For every real number a, a * 1 = a. |
Inverse Property of Multiplication | For every nonzero real number a, there is a multiplicative inverse 1/a such that a(1/a) = 1. |
Distributive Property | For every real number a, b, and c,
a(b + c) = ab + ac
a(b - c) = ab - ac
(b + c)a = ba + ca
(b - c)a = ba - ca |
Multiplication Property of Zero | For every real number n, n * 0 = 0. |
Multiplication Property of -1 | For every real number n, -1 * n = -n |
Commutative Property of Addition | For every real number a and b,
a + b = b + a |
Commutative Property of Multiplication | For every real number a and b,
a * b = b * a |
Associative Property of Addition | For every real number a, b, and c,
(a + b) + c = a + (b + c) |
Associative Property of Multiplication | For every real number a, b, and c,
(a * b) * c = a * (b * c) |