[tex]\bf \stackrel{mixed}{3\frac{5}{9}}\implies \cfrac{3\cdot 9+5}{9}\implies \stackrel{improper}{\cfrac{32}{9}}~\hfill \stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{32}{9}\div \cfrac{8}{3}\implies \cfrac{\stackrel{4}{~~\begin{matrix} 32 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{3}{~~\begin{matrix} 9 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{4}{3}\implies 1\frac{1}{3}[/tex]
