## Distributive, Identity, and Inverse Properties

### Distributive, Identity, and Inverse Properties: Learn

An **Axiom** is a mathematical statement that is assumed to be true.
A **Property** can be proven logically from axioms.

**Distributive Property**: This is the only property which
combines both addition and multiplication.

For examples x(y + z) = xy + xz and (y + z)x = yx + zx

**Additive Identity Axiom**: A number plus zero equals that number.
(The number keeps its identity!)

For examples x + 0 = x or 0 + x = x

**Multiplicative Identity Axiom**: A number times 1 equals that number.
(The number keeps its identity!)

For examples x * 1 = x or 1 * x = x

**Additive Inverse Axiom**: The sum of a number and the Additive
Inverse of that number is zero. Every real number has a unique additive inverse.
Zero is its own additive inverse.

For example x + (-x) = 0

**Multiplicative Inverse Axiom**: The product of a real number
and its multiplicative inverse is 1. Every real number has a unique
multiplicative inverse. The reciprocal of a nonzero number is the
multiplicative inverse of that number. Reciprocal of x is 1/x.

For example x * 1/x = 1

### Distributive, Identity, and Inverse Properties: Practice

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