The value of $$\frac{5\frac{1}{2} \div 3\frac{2}{3} of \frac{1}{4} + \left(5\frac{1}{9} - 7\frac{7}{8} \div 9\frac{9}{20}\right) \times \frac{9}{11}}{5 \div 5 of \frac{1}{10} - 10 \times 10 \div 20}$$ is:

$$\frac{5\frac{1}{2} \div 3\frac{2}{3} of \frac{1}{4} + \left(5\frac{1}{9} - 7\frac{7}{8} \div 9\frac{9}{20}\right) \times \frac{9}{11}}{5 \div 5 of \frac{1}{10} - 10 \times 10 \div 20}$$

= $$\frac{\frac{11}{2} \div \frac{11}{3} of \frac{1}{4} + \left(\frac{46}{9} - \frac{63}{8} \div \frac{189}{20}\right) \times \frac{9}{11}}{5 \div 5 of \frac{1}{10} - 10 \times 10 \div 20}$$

= $$\frac{\frac{11}{2} \div \frac{11}{12} + \left(\frac{46}{9} - \frac{63}{8} \div \frac{189}{20}\right) \times \frac{9}{11}}{5 \div \frac{1}{2} - 10 \times 10 \div 20}$$

= $$\frac{ 6 + \left(\frac{46}{9} - \frac{5}{6}\right) \times \frac{9}{11}}{10 - 10 \times 0.5}$$

= $$\frac{ 6 + \left( \frac{77}{18}\right) \times \frac{9}{11}}{5}$$

= $$\frac{ 6 + ( \frac{7}{2})}{5}$$

=$$\frac{19}{10} = 1 \frac{9}{10}$$