32. 2/3 : 9/14 4/5 : 15/16 3/7 : 8/21 12/23 : 1 17/39 : 0 2/5 : 4/5 3/7 : 9/14 5/8 : 1/40 3/17 : 2/51 2/11 : 4/77 3/4 : 2

Решение:

1. \(\frac{2}{3} : \frac{9}{14} = \frac{2}{3} \times \frac{14}{9} = \frac{28}{27}\)
2. \(\frac{4}{5} : \frac{15}{16} = \frac{4}{5} \times \frac{16}{15} = \frac{64}{75}\)
3. \(\frac{3}{7} : \frac{8}{21} = \frac{3}{7} \times \frac{21}{8} = \frac{3 \times 3}{8} = \frac{9}{8}\)
4. \(\frac{12}{23} : 1 = \frac{12}{23}\)
5. \(\frac{17}{39} : 0\) — деление на ноль невозможно.
6. \(\frac{2}{5} : \frac{4}{5} = \frac{2}{5} \times \frac{5}{4} = \frac{2}{4} = \frac{1}{2}\)
7. \(\frac{3}{7} : \frac{9}{14} = \frac{3}{7} \times \frac{14}{9} = \frac{3 \times 2}{9} = \frac{6}{9} = \frac{2}{3}\)
8. \(\frac{5}{8} : \frac{1}{40} = \frac{5}{8} \times 40 = 5 \times 5 = 25\)
9. \(\frac{3}{17} : \frac{2}{51} = \frac{3}{17} \times \frac{51}{2} = \frac{3 \times 3}{2} = \frac{9}{2}\)
10. \(\frac{2}{11} : \frac{4}{77} = \frac{2}{11} \times \frac{77}{4} = \frac{2 \times 7}{4} = \frac{14}{4} = \frac{7}{2}\)
11. \(\frac{3}{4} : 2 = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}\)

Ответ:
\(\frac{28}{27}\), \(\frac{64}{75}\), \(\frac{9}{8}\), \(\frac{12}{23}\), деление на ноль невозможно, \(\frac{1}{2}\), \(\frac{2}{3}\), 25, \(\frac{9}{2}\), \(\frac{7}{2}\), \(\frac{3}{8}\).