Решение:
1. $$\frac{27}{44} : \frac{45}{77} = \frac{27}{44} \cdot \frac{77}{45} = \frac{27 \cdot 77}{44 \cdot 45} = \frac{3 \cdot 7}{4 \cdot 5} = \frac{21}{20}$$
2. $$\frac{21}{20} - \frac{1}{4} = \frac{21}{20} - \frac{5}{20} = \frac{21 - 5}{20} = \frac{16}{20} = \frac{4}{5}$$
Ответ: **$$\frac{4}{5}$$**