FINDING RECIPROCALS

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

For $\,x\ne 0\,$, the reciprocal of [beautiful math coming... please be patient] $\,x\,$ is $\displaystyle\,\frac{1}{x}\,$.

In particular, the reciprocal of [beautiful math coming... please be patient] $\displaystyle\,\,\frac{a}{b}\,\,$ is [beautiful math coming... please be patient] $\displaystyle\,\,\frac{b}{a}\,\,$.

The number [beautiful math coming... please be patient] $\,0\,$ does not have a reciprocal, since division by zero is not allowed.
For all other numbers, a number multiplied by its reciprocal equals [beautiful math coming... please be patient] $\,1\,$:   $x\cdot \frac1x = 1$

EXAMPLES:
The reciprocal of [beautiful math coming... please be patient] $\,\,5\,\,$ is [beautiful math coming... please be patient] $\displaystyle\,\,\frac{1}{5}\,\,$.
The reciprocal of [beautiful math coming... please be patient] $\displaystyle\,\,\frac{2}{3}\,\,$ is [beautiful math coming... please be patient] $\displaystyle\,\,\frac{3}{2}\,\,$.
The reciprocal of [beautiful math coming... please be patient] $\quad-6\quad$ is [beautiful math coming... please be patient] $\quad\displaystyle-\frac{1}{6}\quad$.
The reciprocal of [beautiful math coming... please be patient] $\displaystyle\quad-\frac{5}{7}\quad$ is [beautiful math coming... please be patient] $\displaystyle\quad-\frac{7}{5}\quad$.
The reciprocal of [beautiful math coming... please be patient] $\,0\,$ 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 .

Find the reciprocal:
    
(MAX is 10; there are 10 different problem types.)