Simplify :

$\Big(2\dfrac{3}{4} + 1\dfrac{5}{6}\Big)$ ÷ $2\dfrac{1}{5}$ of $3\dfrac{1}{3}$

We have:

$\Big(2\dfrac{3}{4} + 1\dfrac{5}{6}\Big)$ ÷ $2\dfrac{1}{5}$ of $3\dfrac{1}{3}$

= $\Big(\dfrac{11}{4} + \dfrac{11}{6}\Big)$ ÷ $\dfrac{11}{5}$ of $\dfrac{10}{3}$ [Converting mixed to improper fraction]

According to BODMAS rule, we simplify brackets first

$\begin{array}{ll} = \Big(\dfrac{33 + 22}{12}\Big) ÷ \dfrac{11}{5} \text{ of } \dfrac{10}{3} \\ = \dfrac{55}{12} ÷ \dfrac{11}{5} \text{ of } \dfrac{10}{3} & \text{[Brackets simplified]} \\ = \dfrac{55}{12} ÷ \dfrac{11}{5} \times \dfrac{10}{3} \\ = \dfrac{55}{12} ÷ \dfrac{110}{15} \\ = \dfrac{55}{12} ÷ \dfrac{22}{3} & \text{[Of simplified]} \\ = \dfrac{55}{12} \times \dfrac{3}{22} & [\text{Reciprocal of } \dfrac{22}{3} \text{ is } \dfrac{3}{22}] \\ = \dfrac{5}{12} \times \dfrac{3}{2} & \text{[Dividing 55 and 22 by 11]} \\ = \dfrac{15}{24} = \dfrac{5}{8} & \text{[Division simplified]} \end{array}$

∴ The answer is $\dfrac{5}{8}$