Reciprocal of a fraction

If we swap the numerator and the denominator in the fraction #\dfrac{2}{3}#, we get #\dfrac{3}{2}#. We now see that: \[\dfrac{2}{3} \times \dfrac{3}{2} =\dfrac{6}{6} = 1\]

In general, it holds that:

Two numbers are each other's reciprocal (also called inverse) if their product is #1#.

Examples

\begin{array}{rcrcr}\dfrac{3}{5} &\times& \dfrac{5}{3} &=& 1\\\dfrac{1}{10} &\times& 10 &=& 1\\-\dfrac{4}{3} &\times& -\dfrac{3}{4} &=& 1\end{array}