### Instruction: Given that $a$, $b$, and $c$ are nonzero real numbers, find all possible values of the expression
\[\frac{a}{|a|} + \frac{b}{|b|} + \frac{c}{|c|} + \frac{abc}{|abc|}.\]Enter all possible values, separated by commas.### Response: I notice that each term in the expression is either $-1$ or $1$, depending on the sign of the numerator.
If all of $a$, $b$, and $c$ are positive, then each term is $1$, and the expression is $4$.
If one of $a$, $b$, and $c$ is negative, say $a$, then the first term is $-1$, the fourth term is $-1$, and the other two terms are $1$, so the expression is $0$.
If two of $a$, $b$, and $c$ are negative, say $a$ and $b$, then the first two terms are $-1$, the third term is $1$, and the fourth term is $1$, so the expression is $0$ again.
If all of $a$, $b$, and $c$ are negative, then each term is $-1$, and the expression is $-4$.
So the only possible values are $-4$, $0$, and $4$.