Try to give a description of $Q/ \sim$.

You're supposed to recognize it. If you don't, there isn't much to be done. The $Q$ is a hint, though.

We have that $Q/\sim$ is $\Bbb Q$. This is the conventional, formal definition of the rational numbers. A pair $(a,b)\in Q$ corresponds to the fraction $\frac ab$, while $[(a,b)]$ is the collection of all fractions that represent the same rational number, through regular expanding and simplification of fractions.