﻿ Finding Reciprocals
FINDING RECIPROCALS
by Dr. Carol JVF Burns (website creator)
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• PRACTICE (online exercises and printable worksheets)
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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.
Master the ideas from this section

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.)