This a simple (sort of stupid) arithmetic based question that may require just the littlest bit of work.
Consider $\cfrac {x}{a}$
I know that division is the number of times I'll have to remove a quantity $a$ from $x$ to end up with $0$ (the remainder). With $x, a \in \mathbb Z$, and $x > a$, the first encounter may be that $x$ is completely divisible by $a$. Say $\cfrac{4}{2}=2$. I've removed $2$ from $4$ twice. So there, my action was removing $2$. But look at $\cfrac{16}{100}$ or any representation of a decimal ($\in\mathbb R$). In $\cfrac{16}{100}$ I'm removing $100$ from $16$, only $0.16$ times. Now that as a real world action is quite an imaginary thing, no?Although I've divided $x$ by $a$, I've incompletely subtracted $a$ from $x$.
~(Please elaborate on improper fractions too, because I may not have the right basic idea about them)
To sum up my question here, I want to know how am I doing this subtraction incompletely in these cases. How is this working in the real world like in computers and our minds? Do we accept some kinds of operations to work like we accept something abnormal like the Twin slit experiment?