Simplify :

$1\dfrac{1}{6} ÷ 1\dfrac{5}{9} \times 3\dfrac{1}{3}$

Solving,

$\Rightarrow 1\dfrac{1}{6} ÷ 1\dfrac{5}{9} \times 3\dfrac{1}{3}\\[1em] \Rightarrow \dfrac{7}{6} ÷ \dfrac{14}{9} \times \dfrac{10}{3}\\[1em] \Rightarrow \dfrac{7}{6} \times \dfrac{9}{14} \times \dfrac{10}{3}\\[1em] \Rightarrow \dfrac{7}{14} \times \dfrac{9}{3} \times \dfrac{10}{6}\\[1em] \Rightarrow \dfrac{1}{2} \times 3 \times \dfrac{5}{3}\\[1em] \Rightarrow \dfrac{5}{2}\\[1em] \Rightarrow 2\dfrac{1}{2}.$

Hence, $1\dfrac{1}{6} ÷ 1\dfrac{5}{9} \times 3\dfrac{1}{3} = 2\dfrac{1}{2}$.