Решение:

1. $$\frac{7}{15} : \frac{14}{25} = \frac{7}{15} \cdot \frac{25}{14} = \frac{7 \cdot 25}{15 \cdot 14} = \frac{1 \cdot 5}{3 \cdot 2} = \frac{5}{6}$$ Ответ: $$\frac{5}{6}$$
2. $$2\frac{2}{9} : 1\frac{7}{9} = \frac{2 \cdot 9 + 2}{9} : \frac{1 \cdot 9 + 7}{9} = \frac{20}{9} : \frac{16}{9} = \frac{20}{9} \cdot \frac{9}{16} = \frac{20 \cdot 9}{9 \cdot 16} = \frac{5}{4} = 1\frac{1}{4}$$ Ответ: $$1\frac{1}{4}$$
3. $$\frac{8}{13} : 4 = \frac{8}{13} : \frac{4}{1} = \frac{8}{13} \cdot \frac{1}{4} = \frac{8 \cdot 1}{13 \cdot 4} = \frac{2}{13}$$ Ответ: $$\frac{2}{13}$$