Congruence Classes with Reals

Question

Can we say that (1/4 congruent to 2) mod 7? "because 4^5 congruent to 2"

If yes, does that mean 1/4 is member of congruence class [2] (mod 7)? what about 15/4,...?

What does that really mean?

Answer 1

Since every nonzero element (class) has a multiplicative inverse modulo $7$ you can indeed think about things like $1/4$ or $3/5$ or $13/3$ mod $7$. Sometimes that's convenient, sometimes it's confusing.