The Statement of the Problem:
We identify $\mathbb Q$ with the set of equivalence classes $[a,b]$, where $(a,b) \in \mathbb Z \times \mathbb N^+$ and $(a,b) \sim (a'b')$ iff $ab'=ba'$. We define $(a,b) \ge (c,d)$ iff $ad \ge bc$.
i) Show that this relation is well defined on the quotient, i.e. if $(a,b) \sim (a',b')$ and $(c,d) \sim (c',d')$ then $(a,b) \ge (c,d)$ iff $(a',b') \ge (c',d')$.
ii) Which equivalence class represents the zero element $0_{\mathbb Q}$ in $\mathbb Q$? Which elements in $\mathbb Q$ are less than or equal to $0_{\mathbb Q}$?
Where I Am:
So, I'm pretty sure I got part (i), but I don't really understand part (ii). (I included the first part just for context.) Wouldn't it just be when $a$ or $b$ equals $0$ because then you'd have multiplication by $0$? That doesn't seem right to me. If anyone could steer me in the right direction, I'd appreciate it. Thanks.
The question can be translated into: what equivalence class is the neutral element under addition? That is, describe $0_\mathbb{Q}=[a_0,b_0]$ such that for any $[a,b]\in\mathbb{Q}$ we have: $$[a_0,b_0]+[a,b]=[a,b].$$ I think you can take it from here.