Question

When the whole is the same why does it take 4 copies of 1 tenth to equal 2 copies of 1 fifth

Answer 1

       In summary, the "whole" can be split up differently and different parts are greater than or less than other parts.

$\frac{1}{10}$ is smaller than $\frac{1}{5}$, so it will take more $\frac{1}{10}$s to equal a $\frac{1}{5}$.

       -> The exact value is two $\frac{1}{10}$s per $\frac{1}{5}$

4 copies of 1 tenth = $\frac{4}{10}$

2 copies of 1 fifth = $\frac{2}{5}$

       They are both equal to $\frac{2}{5}$, but $\frac{4}{10}$ is broken up into smaller pieces. This is why it takes more tenths to equal a fifth.

$\frac{4}{10}$ = $\frac{4/2}{10/2} =\frac{2}{5}$ which is equal to $\frac{2}{5}$.