The reciprocal of 4 plus the reciprocal of 5 is the reciprocal of what number?

Jan 8, 2016

$\frac{20}{9}$

Explanation:

In symbols, we want to find $x$, where:

$\frac{1}{x} = \frac{1}{4} + \frac{1}{5}$

To add two fractions, re-express them with the same denominator, then add then numerators...

$\frac{1}{4} + \frac{1}{5} = \frac{5}{20} + \frac{4}{20} = \frac{9}{20}$

So $x = \frac{1}{\frac{1}{4} + \frac{1}{5}} = \frac{1}{\frac{9}{20}} = \frac{20}{9}$