Inverse Operation is an operation that reverses or undo the effect of another operation.

Table of Contents

## Definition of Inverse Operation

What are Inverse Operations?

Inverse means reverse in position / direction. The word “inverse” comes from the Latin word “inversus” which means to turn inside out or upside down. Inverse operation in mathematics is an operation that undoes what was done by the previous operation. Most operations have an inverse.

There are four main mathematical operations. They are addition, subtraction, multiplication, and division. The inverse of addition is subtraction, & vice versa. The inverse of multiplication is division, & vice versa.

Let’s look at some examples to show how inversion works.

Take this simple addition problem:

7 + 4 = 11

If we want to reverse the addition, we just subtract 11 – 4 = 7, So we are back to where we started.

The same is true for multiplication and division:

5 × 6 = 30 and 30 / 6 = 5.

## Properties of Inverses

There are 4 mathematical properties for inverses Operation.

### Additive Inverse Property

when you add a number to its opposite, the result is always 0.

x + (-x) = 0

### Multiplicative Inverse Property

when you multiply any number except zero by its opposite, the result is always 1.

x × (1/x) = 1

### Additive Property

when you add any number to zero, the result is the same number.

x + 0 = x

### Multiplicative Property

when you multiply any number by 1, the number does not change.

x × 1 = x

## Examples

Example | |

Additive Inverse Property | 4 + (-4) = 0 |

Multiplicative Inverse Property | 7 × (1/7) = 1 |

Additive Property | 7 + 0 = 7 |

Multiplicative Property | 13 × 1 = 13 |