# Identity element

An identity element is a number that, when used in an operation with another number, leaves that number the same.

### identity property for addition

The identity property for addition dictates that the sum of 0 and any other number is that number.

Examples

Ex. 1: | 27 + 0 | = | 0 + 27 | = | 27 |

Ex. 2: | 3 + 0 | = | 0 + 3 | = | 3 |

The identity property for addition may be written as:

a + 0 = 0 + a = a

### identity property for multiplication

The identity property for multiplication dictates that the product of 1 and any number equals that number.

Example

8 × 1 = 1 × 8 = 8

The identity property for multiplication may be written as:

a × 1 = 1 × a = a