What is the inverse of a number? Is it the same as calculating its opposite? Use our online calculator and get the inverse of any quantity immediately. Just type the number of which you want to calculate its opposite, press the calculate button and you will automatically get the result on the screen.

If you want to know more about what the inverse of a number is and **how it is calculated**read on.

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## What is the inverse of a number?

The inverse of a number **is equal to another number obtained by solving the operation 1/x**where x is the initial number.

**The inverse of a number should not be confused with its opposite.**. While the inverse is 1/x, the opposite is equal to -x. That is, the inverse of 2 is equal to 1/2 while its opposite will be equal to -2.

To differentiate between the two concepts, here are a couple of "tricks" or rules that will help us remember the difference between the opposite and the inverse of a number:

- The inverse of a number multiplied by the number gives us 1 as the result. Example:

3 x 1/3 = 1

- The opposite of a number added with the number itself gives us 0 as a result. Example:

3 + (-3) = 0

## How to calculate the inverse of a number

As we have already seen in the previous point, the inverse of a number x is calculated by the formula 1/x. To make it clear, we are going to see some examples of the calculation of inverse numbers:

Number (x) | Inverse (1/x) | Opposite (-x) |
---|---|---|

2 | 1/2 =0,5 | -2 |

3 | 1/3 = 0,33 | -3 |

5 | 1/5 = 0,2 | -5 |

-5 | 1/-5 = -0,2 | 5 |

As you can see, the operation is simple and does not involve any difficulty. **If the number is negative, it is calculated in exactly the same way.**

## What is the inverse of 0?

The inverse of zero **does not exist.**Why? This is because any number divided by zero gives us an indeterminacy whose value is infinite.

1/0 = ∞

For a better understanding, in the graph above you can see a representation of what happens when we try to calculate the inverse of zero from the left and from the right, obtaining as a result that the inverse is -∞ and +∞ respectively.

For all these reasons, we can see some **properties of the inverse function**:

- Not defined when x = 0
- For values of x greater than 0 (x > 0), the function takes positive values. As we increase the value of x, the function approaches zero.
- For values of x less than 0 (x < 0), the function takes negative values. If we approach negative values closer and closer to -∞, the function approaches zero.
- It is a symmetric function with respect to the origin and with respect to the bisector that turns the second and fourth quadrant.
- The inverse of the inverse is the same number. For example, if we want to calculate the inverse of the inverse of the inverse of 9, we have that:

1/1/9 = 9

## How to calculate the inverse of a number with the calculator

If you have a scientific calculator nearby, you can easily calculate the inverse of a number. Just locate the key with "x" engraved on it.^{-1}(the one we've circled in red in the photo above).

If your calculator has such a key, you will be able to do the inverse function of any number in a much more comfortable way. For example, if we want to calculate the inverse of 8, the sequence of keys to press will be as follows:

8 → x

^{-1}→ =

Inverse fraction

If we are asked to calculate the inverse of a fraction, we simply have to flip it around, i.e:

- The numerator becomes the denominator
- The denominator becomes the numerator

We do not have to do any kind of operation. Let's see it with several solved exercises:

- The inverse fraction of 4/5 is 5/4.
- The inverse fraction of 4/7 is 7/4.

## Inverse matrix

If you want to **calculate the inverse matrix**, below we leave you with the calculators to solve them according to their dimensions. In each of these pages you will find the explanation of how to do it with solved examples and more.