Find the integer $n$, $0 \le n \le 11$, such that \[n \equiv 10389 \pmod{12}.\]
I know that the notation $n \equiv 10389 \pmod{12}$ means that $n$ and $10389$ have the same remainder when divided by $12$. I can write $10389 = 12q + r$, where $q$ is the quotient and $r$ is the remainder, and $0 \le r < 12$. I can use long division or a calculator to find that $q = 865$ and $r = 9$. So $10389 = 12 \cdot 865 + 9$, and $9$ is the remainder when I divide $10389$ by $12$. This means that $n \equiv 9 \pmod{12}$, and since $0 \le n \le 11$, the only possible value for $n$ is $9$. 