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.
1/2 + 1 1/2 + 1/3. you need to change them so that they all have a common denominator and that would be 3/6 + 1 3/6 + 2/6. that's gives you 1 8/6 which equals 2 2/6 which in simplest form is 2 1/3