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'Keep it Simple' printed from https://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 $\frac{1}{16}$?