\(\begin{array}{l}
\frac{{11}}{{12}} + \frac{{19}}{{20}} + \frac{{29}}{{30}} + \frac{{41}}{{42}} + \frac{{55}}{{56}} + \frac{{71}}{{72}} + \frac{{89}}{{90}} + \frac{{109}}{{110}}\\
 = 1 - \frac{1}{{12}} + 1 - \frac{1}{{20}} + 1 - \frac{1}{{30}} + 1 - \frac{1}{{42}} + 1 - \frac{1}{{56}} + 1 - \frac{1}{{72}} + 1 - \frac{1}{{90}} + 1 - \frac{1}{{110}}\\
 = \left( {1 + 1 + 1 + ... + 1} \right) - (\frac{1}{{12}} + \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} + \frac{1}{{90}} + \frac{1}{{110}})\\
 = 8 - (\frac{{4 - 3}}{{3.4}} + \frac{{5 - 4}}{{4.5}} + \frac{{6 - 5}}{{5.6}} + \frac{{7 - 6}}{{6.7}} + \frac{{8 - 7}}{{7.8}} + \frac{{9 - 8}}{{8.9}} + \frac{{10 - 9}}{{9.10}} + \frac{{11 - 10}}{{10.11}})\\
 = 8 - (\frac{1}{3} - \frac{1}{4} + \frac{1}{4} - \frac{1}{5} + \frac{1}{5} - \frac{1}{6} + \frac{1}{6} - \frac{1}{7} + \frac{1}{7} - \frac{1}{8} + \frac{1}{8} - \frac{1}{9} + \frac{1}{9} - \frac{1}{{10}} + \frac{1}{{10}} - \frac{1}{{11}})\\
 = 8 - (\frac{1}{3} - \frac{1}{{11}})\\
 = 8 - \frac{{11 - 3}}{{33}}\\
 = 8 - \frac{8}{{33}}\\
 = \frac{{264 - 8}}{{33}}\\
 = \frac{{256}}{{33}}
\end{array}\)