# Finding Reciprocals

Here, you will practice finding reciprocals (multiplicative inverses) of whole numbers and fractions.

For $\,x\ne 0\,,$ the reciprocal of $\,x\,$ is $\displaystyle\,\frac{1}{x}\,.$

In particular, the reciprocal of $\displaystyle\,\,\frac{a}{b}\,\,$ is $\displaystyle\,\,\frac{b}{a}\,\,.$

The number $\,0\,$ does not have a reciprocal, For all other numbers, a number multiplied by its reciprocal equals $\,1\,$:   $x\cdot \frac1x = 1$

## Examples

The reciprocal of $\,\,5\,\,$ is $\displaystyle\,\,\frac{1}{5}\,\,.$
The reciprocal of $\displaystyle\,\,\frac{2}{3}\,\,$ is $\displaystyle\,\,\frac{3}{2}\,\,.$
The reciprocal of $\quad-6\quad$ is $\quad\displaystyle-\frac{1}{6}\quad$.
The reciprocal of $\displaystyle\quad-\frac{5}{7}\quad$ is $\displaystyle\quad-\frac{7}{5}\quad$.
The reciprocal of $\,0\,$ is not defined. Zero is the only real number which does not have a reciprocal.

## Practice

Type in   nd   (uppercase or lowercase) if the reciprocal is not defined. Type fractions using a diagonal slash:   for example,  1/3 .