Question

by what no. should 5/9 be divided to get 3/5

Answer 1

Let the number which should be divided by 5/9 to get 3/5 is x.
Therefore
5/9 ÷ x = 3/5
5/9 * 1/x = 3/5
5/9x = 3/5
25 = 27x
x = 25/27

The number is 25/27 

Answer 2

let the unknown number be X
5/9/X=3/5
=5/9×1/X=3/5
5/9x=3/5
25=27x
X=25/27
this is the answer