The value of $$2\frac{7}{8} \div \left(3\frac{5}{6} \div \frac{2}{7}  of  2\frac{1}{3}\right) \times \left[\left(2\frac{6}{7}  of  4\frac{1}{5} \div \frac{2}{3}\right) \times \frac{5}{9}\right]$$ is:

Given that,

$$2\frac{7}{8} \div \left(3\frac{5}{6} \div \frac{2}{7} of 2\frac{1}{3}\right) \times \left[\left(2\frac{6}{7} of 4\frac{1}{5} \div \frac{2}{3}\right) \times \frac{5}{9}\right]$$

$$\Rightarrow 2\frac{7}{8} \div \left(3\frac{5}{6} \div \frac{2}{7} of 2\frac{1}{3}\right) \times \left[\left(\frac{20}{7} of \frac{21}{5} \div \frac{2}{3}\right) \times \frac{5}{9}\right]$$

$$\Rightarrow 2\frac{7}{8} \div \left(3\frac{5}{6} \div \frac{2}{7} of 2\frac{1}{3}\right) \times \left[\left(\frac{20\times 21}{7\times 5} \div \frac{2}{3}\right) \times \frac{5}{9}\right]$$

$$\Rightarrow 2\frac{7}{8} \div \left(3\frac{5}{6} \div \frac{2}{7} of 2\frac{1}{3}\right) \times \left[\left(\frac{20\times 21\times 3}{7\times 5\times 2}\right) \times \frac{5}{9}\right]$$

$$\Rightarrow 2\frac{7}{8} \div \left(3\frac{5}{6} \div \frac{2}{7} of 2\frac{1}{3}\right) \times 10$$

$$\Rightarrow 2\frac{7}{8} \div \left(\frac{23}{6} \div \frac{2}{7} of \frac{7}{3}\right) \times 10$$

$$\Rightarrow 2\frac{7}{8} \div \left(\frac{23}{6} \div \frac{2}{3}\right) \times 10$$

$$\Rightarrow \frac{23}{8} \div \left(\frac{23\times 3}{6\times 2}\right) \times 10$$

$$\Rightarrow \frac{23}{8} \div \left(\frac{23}{4}\right) \times 10$$

$$\Rightarrow \frac{23\times 4}{8\times 23} \times 10$$

$$\Rightarrow 5$$