6)175.22

$$17\frac{5}{14}:2\frac{2}{27}=\frac{17 \cdot 14 + 5}{14}:\frac{2 \cdot 27 + 2}{27}=\frac{238+5}{14}:\frac{54+2}{27}=\frac{243}{14}:\frac{56}{27}=\frac{243}{14} \cdot \frac{27}{56}=\frac{243 \cdot 27}{14 \cdot 56}=\frac{6561}{784}=8\frac{209}{784}$$

Ответ: $$8\frac{209}{784}$$