SUGAR MILLS HIGH SCHOOL

Suppose that x, y, and z are numbers.

The Commutative Laws

The Commutative Law of Addition

The Commutative Law of Multiplication

The Associative Laws

The Associative Law of Addition

The Associative Law of Multiplication

The Distributive Law

The Identity Properties

The Zero Property

There exists a number, , such that

The Multiplicative Identity Property

There exists a number, , such that for any number , Multiplying one by a number results in that number.

To be complete, we state also that .

Inverse Properties

The Additive Inverse

For any number , there exists a number x such that

The Multiplicative Inverse

If is any number except 0, there exists a number x such that

Laws of Equality

The Reflexive Property:

The Symmetric Property:

If , then

The Transitive Property:

If , and , then

If , then

If , then

Laws of Inequality

If , then

If and , then

If and , then