Numbers: Fractions
Reciprocal of a fraction
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}
#{{3}\over{2}}#
If we swap the numerator and the denominator of the fraction #{{2}\over{3}}#, we find #{{3}\over{2}}#. To double-check, we multiply the numbers and check if the product equals #1#.
\[{{2}\over{3}} \times {{3}\over{2}}=1\]
Therefore, the reciprocal of #{{2}\over{3}}# equals #{{3}\over{2}}#.
If we swap the numerator and the denominator of the fraction #{{2}\over{3}}#, we find #{{3}\over{2}}#. To double-check, we multiply the numbers and check if the product equals #1#.
\[{{2}\over{3}} \times {{3}\over{2}}=1\]
Therefore, the reciprocal of #{{2}\over{3}}# equals #{{3}\over{2}}#.
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