Zero in Division

Zero divided by any number that is not zero is 0. $\frac{0}{5}$ is 0, because $0\cdot 5$ is 0: multiplying back checks it. The same goes for $\frac{0}{-8}$. Sharing nothing among any number of people gives everyone nothing.

Dividing by zero is different. $\frac{5}{0}$ would have to be a number that makes 5 when multiplied by 0. But every number times 0 is 0, never 5, so no such number exists. Division by zero is undefined: it has no answer at all.

So the place of the zero is what matters. Zero on top of the bar is fine and gives 0. Zero underneath the bar has no answer, which is why a calculator shows an error when you try it.