# Reciprocal

The reciprocal of a number is one divided by that number. It is the same as raising it to the power $$-1$$

The reciprocal of $$3$$ is a third. It can be written as $$1/3$$ or $$3^{-1}$$.

The **reciprocal of a fraction** is found by swapping the numerator and the denominator.

These are the **main properties** of the reciprocal:

- Every real number except for zero has a reciprocal.
- The reciprocal of a number has the same sign as the number.
- The reciprocal of the reciprocal is the original number.
- The reciprocal multiplied by the original number is $$1$$.
- The reciprocal of a positive number between $$0$$ and $$1$$ is larger than $$1$$, and vice versa.
- The reciprocal of a negative number between $$0$$ and $$-1$$ is less than $$-1$$, and vice versa.

A graph showing $$y$$ and the reciprocal of $$x$$