How do you determine the the equivalence classes for a relation on a product set?
Background:
Let $S=\left\{1,2,3,4\right\}$ and $A=S\times S$. The relation $R$ on $A$ can be defined by
$$\left(a,b\right)R\left(c,d\right) \iff a/b =c/d$$
For example:
$$\left(1,2\right)R\left(2,4\right) \text{ since } 1/2 = 2/4$$
Assuming $R$ is an equivalence relation, what are the equivalence classes for $A/R$?