The value of $$\frac{2}{3} \times \frac{3}{{\frac{5}{6} \div \frac{2}{3}{\text{ of 1}}\frac{1}{4}}} = ?$$

$$\eqalign{ & {\text{According to question,}} \cr & \,\,\,\,\,\,\frac{2}{3} \times \frac{3}{{\frac{5}{6} \div \frac{2}{3}{\text{of 1}}\frac{1}{4}}} \cr & \Rightarrow \frac{2}{3} \times \frac{3}{{\frac{5}{6} \div \left( {\frac{2}{3} \times \frac{5}{4}} \right)}} \cr & \Rightarrow \frac{2}{3} \times \frac{3}{{\frac{5}{6} \div \frac{5}{6}}} \cr & \Rightarrow \frac{2}{3} \times \frac{3}{1} \cr & \Rightarrow 2 \cr} $$