The value of $$1\frac{1}{8} \div \left(4\frac{1}{4} \div \frac{3}{5} of 8\frac{1}{2}\right) - \frac{2}{5} \times 1\frac{1}{3} \div \frac{4}{5} of 1\frac{2}{3} + \frac{11}{20}$$ is:

$$1\frac{1}{8} \div \left(4\frac{1}{4} \div \frac{3}{5} of 8\frac{1}{2}\right) - \frac{2}{5} \times 1\frac{1}{3} \div \frac{4}{5} of 1\frac{2}{3} + \frac{11}{20}$$

=  $$\frac{9}{8} \div \left(\frac{17}{4} \div \frac{3}{5} of \frac{17}{2}\right) - \frac{2}{5} \times \frac{4}{3} \div \frac{4}{5} of \frac{5}{3} + \frac{11}{20}$$

= $$\frac{9}{8} \div \left(\frac{17}{4} \div \frac{51}{10}\right) - \frac{2}{5} \times \frac{4}{3} \div \frac{4}{3} + \frac{11}{20}$$

= $$\frac{9}{8} \div \left(\frac{17}{4} \times \frac{10}{51}\right) - \frac{2}{5} \times \frac{4}{3} \times \frac{3}{4} + \frac{11}{20}$$

= $$\frac{9}{8} \div \frac{5}{6} - \frac{2}{5} + \frac{11}{20}$$

= $$\frac{9}{8} \times \frac{6}{5} - \frac{2}{5} + \frac{11}{20}$$

= $$\frac{27}{20} - \frac{2}{5} + \frac{11}{20}$$ = $$\frac{3}{2}$$ = 1$$\frac{1}{2}$$