For all $$a$$, $$n\in Z$$ with $$n\neq 0$$, there exist unique $$q$$,$$r\in Z$$ satisfying $$a = qn + r$$ and $$0\le r<|n|$$. Since $$q$$ and $$r$$ are unique, we use $$\lfloor{a/n}\rfloor$$ to denote $$q$$ and $$a$$ % $$n$$ to denote $$r$$. Hence:
$$a=|\frac{a}{n}|n+(a$$%$$n)$$.
The % symbol is often called the modulo operator. Beware that some programming languages also have a % operator in which a % $$n$$ always has the same sign as a. We will instead use the convention that a % $$n$$ is always always nonnegative.