Hey, wait a minute! This is the kind of stuff I used to do for a living. Actually, as absurd as it may sound; '4 out of 3' is, indeed, a fraction - an improper one! It may, also, be represented by the mixed number, 1 1/3; and, as such, it is an, 'infinite rational number', 1.33333 .... ... .
I'm sorry; it's late; I'm overtired, and ought to be in bed. Here's an interesting math website for people, like me, who like to play with numbers: