Simplify :

$1\dfrac{1}{2}\times2\dfrac{3}{4} ÷ 1\dfrac{4}{7}$ of $2\dfrac{5}{8}$

We have:

$1\dfrac{1}{2}\times2\dfrac{3}{4} ÷ 1\dfrac{4}{7}$ of $2\dfrac{5}{8}$

= $\dfrac{3}{2}\times \dfrac{11}{4}$ ÷ $\dfrac{11}{7}$ of $\dfrac{21}{8}$ [Converting mixed to improper fraction]

According to BODMAS rule, we solve "of" first

$\begin{array}{ll} = \dfrac{3}{2}\times \dfrac{11}{4} ÷ \dfrac{11}{7} \times \dfrac{21}{8} \\ = \dfrac{3}{2}\times \dfrac{11}{4} ÷ \dfrac{11}{1} \times \dfrac{3}{8} \\ = \dfrac{3}{2}\times \dfrac{11}{4} ÷ \dfrac{11 \times 3}{1 \times 8} \\ = \dfrac{3}{2}\times \dfrac{11}{4} ÷ \dfrac{33}{8} & \text{[Of simplified]} \\ = \dfrac{3}{2}\times \dfrac{11}{4} \times \dfrac{8}{33} & [\text{Reciprocal of } \dfrac{33}{8} \text{ is } \dfrac{8}{33}] \\ = \dfrac{3}{2}\times \dfrac{1}{4} \times \dfrac{8}{3} \\ = \dfrac{3}{2}\times \dfrac{1}{1} \times \dfrac{2}{3}\\ = \dfrac{3}{2}\times \dfrac{1 \times 2}{1 \times 3} \\ = \dfrac{3}{2}\times \dfrac{2}{3} & \text{[Division simplified]} \\ = \dfrac{6}{6} = 1 & \text{[Multiplication simplified]} \\ \end{array}$

∴ The answer is 1