Question

What fraction is halfway between 1/3 and 1/5?

Answer 1

`4/15`

Explanation:

A trick question: The obvious, but wrong answer is `1/4`.

Actually `1/4` is called the harmonic mean of `1/3` and `1/5` - being the reciprocal of the average of the reciprocals.

To find the number halfway between `a` and `b`, calculate `1/2(a+b)` ...

`1/2(1/3+1/5) = 1/2(5/15+3/15) = 1/2(8/15) = 4/15`

Note that to add the fractions `1/3` and `1/5` we first give them a common denominator `15` by multiplying them by `5/5` and `3/3` respectively. Once we have a common denominator, then we can just add the numerators.