Algebra 1 Properties
Associative Property of Addition
(a + b) + c = a + (b + c) The way in which you group three or more numbers when adding does not change the sum.
Associative Property of Multiplication
(a • b) • c = a • (b • c) The way in which you group three or more numbers when multiplying does not change the product.
Substitution Property
If a = b then a may be replaced by b in any expression. A quantity may be substituted for its equal in any expression.
Additive Inverse
a + (-a) = 0 For a number a, any number that, when added to a, gives a sum of 0.
Additive Identity
a + 0 = a For any number a, the sum of a and 0 is a.
Commutative Property of Addition
a + b = b + a The order in which numbers are added does not change their sum.
Reflexive Property
a = a Any quantity is equal to itself.
Distributive Property
a • (b + c) = a • b + a • c and a • (b - c) = a • b - a • c
Multiplicative Property of Zero
a • 0 = 0 For any number a, the product of a and 0 is 0.
Multiplicative Identity
a • 1 = a For any number a, the product of a and 1 is a.
Commutative Property of Multiplication
a • b = b • a The order in which numbers are multiplied does not change their product
Multiplicative Inverse
a/b • b/a = 1 For every number a/b, where a, b ≠ 0, there is exactly one number b/a, such that the product of a/b and b/a is 1.
Symmetric Property
if a = b then b = a If one quantity equals a second quantity, then the second quantity equals the first.
Transitive Property
if a = b and b = c then a = c If one quantity equals a second quantity and the second quantity equals a third quantity, then the first quantity equals the third quantity.
