Why does $\frac{5}{4} + \frac{2}{3}$ need to be rewritten as $\frac{15}{12} + \frac{8}{12}$ to be added? It's not obvious.

I'm looking towards the fact that any integer can be rewritten as $x=qy$ but these work for rational numbers as well.

Can anyone clarify why exactly fraction addition works only when you find a common denominator?