# Arithmetic properties

Here are a list of arithmetic properties.

### Addition

In mathematics, there are five properties that involve addition.

**Commutative Property of Addition**

When two numbers are added, the result will be the same regardless of the order. For example:

**Associative Property of Addition**

When a quantity of numbers greater than three are added together, the result will be the same no matter which order the numbers were added in. For example:

**Identity Property of Addition**

The sum of any number(positive or negative, fraction, decimal, etc) and zero will equal that number. Of course, . Other examples include: and .

**Additive Inverse Property**

Very simple, , or vice versa. A number plus another number equals zero.

**Distributive Property**

Note that this is the only property in which both addition and multiplication are used. When the sum of two numbers is multiplied by a third number, the product is equal to each addend multiplied by the same third number. For example: .

### Multiplication

There are four properties that involve multiplication, plus the distributive property which also involves addition.

**Commutative Property of Multiplication**

When two numbers are multiplication, the product will be the same regardless of the order they were multiplied in. For example:

**Associative Property of Multiplication"'**

Basically the same as the associative property of addition, except you are using multiplication instead. For example:

**Multiplicative Identity**

The product of any number and one is the number. For example:

**Multiplicative Inverse**

A number multiplied by another number equals one. For example: