Simplify :

$\dfrac{1}{3}$ of $4\dfrac{2}{3} ÷ 2\dfrac{1}{3}\times 1\dfrac{1}{2}$

We have:

$\dfrac{1}{3}$ of $4\dfrac{2}{3}$ ÷ $2\dfrac{1}{3}\times 1\dfrac{1}{2}$

= $\dfrac{1}{3}$ of $\dfrac{14}{3}$ ÷ $\dfrac{7}{3}\times \dfrac{3}{2}$ [Converting mixed to improper fraction]

According to BODMAS rule, we solve "of" first

$\begin{array}{ll} = \dfrac{1}{3} \times \dfrac{14}{3} ÷ \dfrac{7}{3}\times \dfrac{3}{2} \\ = \dfrac{1 \times 14}{3 \times 3} ÷ \dfrac{7}{3}\times \dfrac{3}{2} \\ = \dfrac{14}{9} ÷ \dfrac{7}{3}\times \dfrac{3}{2} & \text{[Of simplified]} \\ = \dfrac{14}{9} \times \dfrac{3}{7}\times \dfrac{3}{2} & [\text{Reciprocal of } \dfrac{7}{3} \text{ is }s \dfrac{3}{7}] \\ = \dfrac{14}{3} \times \dfrac{1}{7} \times \dfrac{3}{2} \\ = \dfrac{2}{3} \times \dfrac{1}{1} \times \dfrac{3}{2} \\ = \dfrac{2 \times1}{3 \times 1} \times \dfrac{3}{2} = \dfrac{2}{3} \times \dfrac{3}{2} & \text{[Division simplified]} \\ = \dfrac{2 \times 3}{3 \times 2} = \dfrac{6}{6}\\ = \dfrac{1}{1} = 1 & \text{[Multiplication simplified]} \end{array}$

∴ The answer is 1