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.

`(1)/(10)` is smaller than
`(1)/(5)`, so it will take more
`(1)/(10)`s to equal a
`(1)/(5)`.

-> The exact value is two
`(1)/(10)`s per
`(1)/(5)`

4 copies of 1 tenth =
`(4)/(10)`

2 copies of 1 fifth =
`(2)/(5)`

They are both equal to
`(2)/(5)`, but
`(4)/(10)` is broken up into smaller pieces. This is why it takes more tenths to equal a fifth.

`(4)/(10)` =
`(4/2)/(10/2) =(2)/(5)` which is equal to
`(2)/(5)`.