What's the next fraction after 45/60

You could say 46/60 (both of these fractions can be reduced), but we can find a fraction between 45/60 and 46/60, namely 91/120. And we can find another between 45/60 and 91/120, and so on ad infinitum.

To answer your question, there is no next fraction. Infinitely many may be found between any two.

45/60 + 1/60 = 46/60 (23/30)