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'The Greedy Algorithm' printed from http://nrich.maths.org/

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Is your fraction bigger than $\frac{1}{2}$?
If not, is it bigger than $\frac{1}{3}$?
If not, is it bigger than $\frac{1}{4}$?
...
Now subtract the largest unit fraction you can.



Here's another example of the Greedy Algorithm at work...

$\frac{4}{5} = \frac{1}{2} + \frac{3}{10}$

$\frac{3}{10} = \frac{1}{4} + \frac{1}{20}$

so

$\frac{4}{5} = \frac{1}{2} + \frac{1}{4} + \frac{1}{20}$



If you're not sure which is bigger, you could use a calculator and convert your fractions into decimals.