## 'Keep it Simple' printed from http://nrich.maths.org/

Try working systematically through all the possibilities.

$\frac{1}{8} = \frac{1}{9} + ?$

$\frac{1}{8} = \frac{1}{10} + ?$

$\frac{1}{8} = \frac{1}{11} + ?$

$\frac{1}{8} = \frac{1}{12} + ?$

$\frac{1}{8} = \frac{1}{13} + ?$

$\frac{1}{8} = \frac{1}{14} + ?$

$\frac{1}{8} = \frac{1}{15} + ?$

$\frac{1}{8} = \frac{1}{16} + ?$ (but this won't count)

Why is $\frac{1}{9}$ the first one you can use?
Why don't you need to go further than $\frac{1}{16}$?