I want to calculate $\frac{\overline{2}}{\overline{3}}$, $\frac{\overline{1}}{\overline{9}}$, $\frac{\overline{32}}{\overline{9}}$ in $\mathbb{Z}_7$.
About first example my book says: $\overline{3}*\overline{5}=\overline{15}=\overline{1}$, then $\frac{\overline{1}}{\overline{3}}=\overline{5}$; and finally $\frac{\overline{2}}{\overline{3}}=\overline{10}=\overline{3}$. It's pretty clear, except first step? From where 5 and 3 came out?
Regards