The value of $$\frac{3}{4} \times 2\frac{2}{3} \div \frac{5}{9}{\text{ of }}1\frac{1}{5} + \frac{2}{{23}} \times 3\frac{5}{6} \div \frac{2}{7}{\text{ of }}2\frac{1}{3}$$        is:

Solution (By Examveda Team)

$$\eqalign{ & \frac{3}{4} \times 2\frac{2}{3} \div \frac{5}{9}{\text{ of }}1\frac{1}{5} + \frac{2}{{23}} \times 3\frac{5}{6} \div \frac{2}{7}{\text{ of }}2\frac{1}{3} \cr & = \frac{3}{4} \times \frac{8}{3} \div \frac{5}{9}{\text{ of }}\frac{6}{5} + \frac{2}{{23}} \times \frac{{23}}{6} \div \frac{2}{7}{\text{ of }}\frac{7}{3} \cr & = \frac{3}{4} \times \frac{8}{3} \div \frac{2}{3} + \frac{2}{{23}} \times \frac{{23}}{6} \div \frac{2}{3} \cr & = \frac{3}{4} \times \frac{8}{3} \times \frac{3}{2} + \frac{2}{{23}} \times \frac{{23}}{6} \div \frac{2}{3} \cr & = 3 + \frac{1}{2} \cr & = 3\frac{1}{2} \cr} $$