PLEASE DO NOT INCLUDE THE CORRECT ANSWER IN THE ORIGINAL POST.
It kills the fun. I saw an ans in some other post by you too, so ....
If m and n are positive integers, and if p and q are different prime number, do p/q and n/m represent different number?
1. Neither n nor m is a prime number.
Case 1: p=2; q=3; n=4; m=6; p/q = n/m
Case 2 n=4; m=5; p/q <> n/m
2. m is not divisible by q
According to (1)Case 1 - we can prove that p/q=n/m. But for this to be true n & m need to be multiple of p & q respectively. Then only the division will lead to an equivalent number. But if, as stated in (2), m is not divisible by q, there is no way that you shall ever get p/q = n/m, because p & q are prime numbers and so the division result can be recreated only by their multiples.
So from 2 we conclude that p/q <> n/m and so it is sufficient.