What does this modular relation mean, if anything? 
Let $x$ and $y$ be real numbers.
Suppose $\dfrac{x}{y \bmod x}$ is a natural number.
What does that say about the relationship between $x$ and $y$?

If $x$ and $y$ are naturals themselves, then I think it means that $x$ is some multiple of $y$ plus some divisor of $y$, but I'm a little fuzzy on what it would mean if $x$ and $y$ are reals.
Thank you.

Assuming that $(y \bmod x) = y - n x$ for some $n \in \mathbb{Z}$ such that $0 \leq y - n x < x$, in the case that $x > 0$, at least.
Then $\dfrac{x}{y \bmod x} = m$ for some integer $m$ means
$$\dfrac{x}{y - n x}=m$$
$$ \Rightarrow (mn+1)x =  m y$$
so we can say, the ratio of $x$ and $y$, where defined, is rational. I'm not sure if anything else less trivial can be said.
