Visually cut a cake 1/5 portions of equal size:
1) divide into half:
2) divide 1/5 of the right half:
3) divide half, obtain 1/5 = right of (3)
$latex \frac{1}{5}= \frac{1}{2} (\frac{1}{2}(1- \frac{1}{5}))= \frac{1}{2} (\frac{1}{2} (\frac{4}{5}))=\frac{1}{2}(\frac{2}{5})$
4) By symmetry another 1/5 at (2)=(4)
5) divide left into 3 portions, each 1/5
$latex \frac{1}{5}= \frac{1}{3}(\frac{1}{2}+ \frac{1}{2}.\frac{1}{5}) = \frac{1}{3}.\frac{6}{10}$
Mathtuition88 