Simplify :

$\Big(22÷5\dfrac{1}{2}\Big)$ ÷ $2\dfrac{1}{5}$ of $3\dfrac{1}{3} + 1\dfrac{5}{11}$

We have:

$\Big(22÷5\dfrac{1}{2}\Big)$ ÷ $2\dfrac{1}{5}$ of $3\dfrac{1}{3} + 1\dfrac{5}{11}$

= $\Big(22÷\dfrac{11}{2}\Big)$ ÷ $\dfrac{11}{5}$ of $\dfrac{10}{3}$ + $\dfrac{16}{11}$ [Converting mixed to improper fraction]

According to BODMAS rule, we simplify brackets first

$\begin{array}{ll} = \Big(22 \times \dfrac{2}{11}\Big) ÷ \dfrac{11}{5}\text{ of }\dfrac{10}{3} + \dfrac{16}{11} & [\text{Reciprocal of } \dfrac{11}{2} \text{ is } \dfrac{2}{11}] \\ = \Big(\dfrac{44}{11}\Big) ÷ \dfrac{11}{5}\text{ of }\dfrac{10}{3} + \dfrac{16}{11} & \text{[Divide 44 and 11 by 11]} \\ = \dfrac{4}{1} ÷ \dfrac{11}{5}\text{ of }\dfrac{10}{3} + \dfrac{16}{11} & \text{[Bracket simplified]} \\ = \dfrac{4}{1} ÷ \dfrac{11}{5} \times \dfrac{10}{3} + \dfrac{16}{11} \\ = \dfrac{4}{1} ÷ \dfrac{110}{15} + \dfrac{16}{11} & \text{[Divide 110 and 15 by 5]} \\ = \dfrac{4}{1} ÷ \dfrac{22}{3} + \dfrac{16}{11} & \text{[Of simplified]} \\ = \dfrac{4}{1} \times \dfrac{3}{22} + \dfrac{16}{11} & [\text{Reciprocal of } \dfrac{22}{3} \text{ is } \dfrac{3}{22}] \\ = \dfrac{12}{22} + \dfrac{16}{11} & \text{[Divide 12 and 22 by 2]} \\ = \dfrac{6}{11} + \dfrac{16}{11} & \text{[Division simplified]} \\ = \dfrac{6 + 16}{11} = \dfrac{22}{11} & \text{[Divide 22 and 11 by 11]} \\ = 2 & \text{[Division simplified]} \end{array}$

∴ The answer is 2