**Решение:**
1) \(9 : \frac{3}{7} = 9 \cdot \frac{7}{3} = \frac{9 \cdot 7}{3} = 3 \cdot 7 = 21\)
2) \(1 : \frac{3}{17} = 1 \cdot \frac{17}{3} = \frac{17}{3} = 5\frac{2}{3}\)
3) \(\frac{9}{32} : 18 = \frac{9}{32} \cdot \frac{1}{18} = \frac{9}{32 \cdot 18} = \frac{1}{32 \cdot 2} = \frac{1}{64}\)
4) \(11 : 3\frac{1}{9} = 11 : \frac{28}{9} = 11 \cdot \frac{9}{28} = \frac{11 \cdot 9}{28} = \frac{99}{28} = 3\frac{15}{28}\)
5) \(2\frac{1}{4} : 3\frac{3}{5} = \frac{9}{4} : \frac{18}{5} = \frac{9}{4} \cdot \frac{5}{18} = \frac{9 \cdot 5}{4 \cdot 18} = \frac{1 \cdot 5}{4 \cdot 2} = \frac{5}{8}\)
6) \(5\frac{5}{6} : \frac{7}{18} = \frac{35}{6} : \frac{7}{18} = \frac{35}{6} \cdot \frac{18}{7} = \frac{35 \cdot 18}{6 \cdot 7} = \frac{5 \cdot 3}{1 \cdot 1} = 15\)
**Ответ:**
1) \(21\); 2) \(5\frac{2}{3}\); 3) \(\frac{1}{64}\); 4) \(3\frac{15}{28}\); 5) \(\frac{5}{8}\); 6) \(15\)