Dear Bridget,

This is excellent question. I guess I had to be more precise in my terminology. Check this out. 

3/x is not a monomial of x, but 3/x=3*(1/x) is a monomial of 1/x. Consider 1/x as a building block. 

I think it is an errata that I wrote down that 3x/y is a monomial, but here is the deal. 

We "can" say that 3x/y is a monomial of "x/y", if we consider "x/y" as a single variable. But, this is not conventional. 

So, I guess you should say 3x/y is not a monomial (of x) or (of y).

However, at your school, it would be clearer because they would ask you a question like "Is this a monomial of x?" In particular, the question usually gives the variable of our interest.

Great question!

Harim Yoo