Найдем сумму:
$$ \frac{5}{11}+\frac{2}{3}+\frac{1}{9}+\frac{6}{11} = (\frac{5}{11} + \frac{6}{11}) + (\frac{2}{3} + \frac{1}{9}) $$
$$ = \frac{5 + 6}{11} + \frac{2 \cdot 3}{3 \cdot 3} + \frac{1}{9} = \frac{11}{11} + \frac{6}{9} + \frac{1}{9} $$
$$ = 1 + \frac{6+1}{9} = 1 + \frac{7}{9} = 1\frac{7}{9} $$
Ответ: $$1\frac{7}{9}$$