Consider the equivalence relation $\sim$ on $\mathbb{Z} \times (\mathbb{Z} \setminus \{0\})$ defined by $(a,b) \sim (c,d)$ if $a \cdot d = b \cdot c$. Describe the equivalence classes in terms of familiar mathematical objects?
The above is a homework problem. I can see some patterns in the equivalence classes, however I'm not sure how to answer or approach the question given. Thanks!
The equivalence classes corespond to rational numbers with $\frac{a}{b}$ representing the class $(a,b)$.