Closure Axiom 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 Axiom 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)

Order of Operations ... Algebraic Hierarchy

1.     Parenthesis, Symbols of Inclusion
2.     Upper level math expressions (powers, roots, sine, cosine, tangent, log, etc.)
3.     Multiplication / Division (from left to right)
4.     Addition / Subtraction (from left to right)


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