Algebra Basic Indentites

Basic Identities
Closure Property of Addition
Sum (or difference) of 2 reals 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)