# Inverse

Inverse means the **opposite in effect**. The reverse of.

Inverse has many meanings in mathematics. Here are a few.

## The Inverse of Adding is Subtracting

Adding moves us one way, subtracting moves us the opposite way.

Example: **20 + 9 = 29** can be reversed by** 29 − 9 = 20** (back to where we started)

And the other way around:

Example: **15 − 3 = 12** can be reversed by** 12 + 3 = 15** (back to where we started)

## Additive Inverse

The **additive inverse** is what we add to a number to **get zero**.

### Example: The additive inverse of −5 is +5, because −5 + 5 = 0.

Another example: the additive inverse of +7 is −7.

## The Inverse of Multiplying is Dividing

Multiplying can be "undone" by dividing.

Example: **5 × 9 = 45** can be reversed by **45 / 9 = 5**

It works the other way around too, dividing can be undone by multiplying.

Example: **10 / 2 = 5 ** can be reversed by **5 × 2 = 10**

## Multiplicative Inverse

The **multiplicative inverse** is what we multiply a number by to get 1.

It is the reciprocal of a number.

### Example: The multiplicative inverse of 5 is \frac{1}{5}, because 5 × \frac{1}{5} = 1

### But Not With 0

You can't divide by 0, so don't try!

### Example: **5 × 0 = 0** cannot be reversed by **0/0 = ???**