You might explain that for any real number $x$, we have $0x=0$. So the equation $0x=0$ has no unique solution. And $0x=1$, for example, has no solution whatsoever. For these reasons, neither $0/0$ nor $1/0$ can be real numbers.

You might explain, at any level, that for any real number $x$, we have $0x=0$. So the equation $0x=0$ has no unique solution. And $0x=1$, for example, has no solution whatsoever. For these reasons, neither $0/0$ (with no unique solution) nor $1/0$ (with no solution) can be real numbers.