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, since division by zero is not allowed.
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.

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Determining if a Product is Positive or Negative

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

(MAX is 10; there are 10 different problem types.)