let's first convert the mixed fractions to improper, and then divide.
[tex] \bf \stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}}\\\\[-0.35em]
~\dotfill\\\\
\cfrac{5}{3}\div \cfrac{4}{5}\implies \cfrac{5}{3}\cdot \cfrac{5}{4}\implies \cfrac{25}{12}\implies 2\frac{1}{12} [/tex]
