Cut a cake 1/5

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

$latex frac{1}{5}= frac{1}{3}(frac{1}{2}+ frac{1}{2}.frac{1}{5}) = frac{1}{3}.frac{6}{10}$