Basic Identities

Basic Identities of Algebra
Closure Property of Addition
Sum (or difference) of 2 real numbers equals a real number

Additive Identity
a + 0 = a

Additive Inverse
a + (-a) = 0

Associative of Addition
(a + b) + c = a + (b + c)

Commutative of Addition
a + b = b + a

Definition of Subtraction
a - b = a + (-b)

Closure Property of Multiplication 
Product (or quotient if denominator 0) of 2 reals equals a real number

Multiplicative Identity
a * 1 = a

Multiplicative Inverse
a * (1/a) = 1 (a 0)

(Multiplication times 0)
a * 0 = 0

Associative of Multiplication
(a * b) * c = a * (b * c)

Commutative of Multiplication
a * b = b * a

Distributive Law
a(b + c) = ab + ac

Definition of Division
a / b = a(1/b)