517 6114,4;

$$\frac{5 \cdot 1}{6} : \frac{7}{11} - 4,4 = \frac{5}{6} \cdot \frac{11}{7} - 4,4 = \frac{55}{42} - 4,4 = \frac{55}{42} - \frac{44}{10} = \frac{55}{42} - \frac{22}{5} = \frac{55 \cdot 5 - 22 \cdot 42}{210} = \frac{275 - 924}{210} = \frac{-649}{210} = -3 \frac{19}{210}$$

Ответ: -649/210