Question

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

Answer 1

`20/9`

Explanation:

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

`1/x = 1/4+1/5`

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

`1/4+1/5=5/20+4/20 = 9/20`

So `x=1/(1/4+1/5) = 1/(9/20) =20/9`