# Expressing a Fraction in Simplest form

I have given a fraction in the form of $p/q$ , i want to express the given fraction as sum of series which is in the form of $1/x$ and $x$ is odd. i.e

$$p/q = 1/x + 1/y+ 1/z+1/l/s$$ such that denominator is an odd number.

One trival way is to express $p/q = 1/q+1/q+1/q+....$($p$ times ). but i want length of the series to less than $p$.

How to do that ?

• Greedy Egyptian algorithm might do. – Ivan Neretin Mar 27 '17 at 10:31
• – mvw Mar 27 '17 at 10:49
• Not a duplicate exactly, as in this post denominators required to be odd. – coffeemath Mar 27 '17 at 11:23
• Can't be less terms than $p$ if $p=1$. – Martin Rattigan Mar 27 '17 at 12:22
• For some fractions $p/q$ it can be done with less than $p$ terms, but based on some empirical tests, whenever it can be done with less than $p$ terms, a greedy odd algorithm will find such a representation with the least number of terms. – quasi Mar 27 '17 at 12:41