5.53. Найдите частное: а) 1/5 : 9/11; б) 1/7 : 5/8; в) 2/7 : 2/9; г) 6/8 : 7/12; д) 4/7 : 16/19; е) 5/9 : 1/2; ж) 12/25 : 8/15; з) 9/14 : 18/35.

1. \(\frac{1}{5}:\frac{9}{11}=\frac{1}{5}\cdot\frac{11}{9}=\frac{11}{45}\).
2. \(\frac{1}{7}:\frac{5}{8}=\frac{1}{7}\cdot\frac{8}{5}=\frac{8}{35}\).
3. \(\frac{2}{7}:\frac{2}{9}=\frac{2}{7}\cdot\frac{9}{2}=\frac{9}{7}=1\frac{2}{7}\).
4. \(\frac{6}{8}:\frac{7}{12}=\frac{3}{4}\cdot\frac{12}{7}=\frac{9}{7}=1\frac{2}{7}\).
5. \(\frac{4}{7}:\frac{16}{19}=\frac{4}{7}\cdot\frac{19}{16}=\frac{19}{28}\).
6. \(\frac{5}{9}:\frac{1}{2}=\frac{5}{9}\cdot2=\frac{10}{9}=1\frac{1}{9}\).
7. \(\frac{12}{25}:\frac{8}{15}=\frac{12}{25}\cdot\frac{15}{8}=\frac{9}{10}\).
8. \(\frac{9}{14}:\frac{18}{35}=\frac{9}{14}\cdot\frac{35}{18}=\frac{5}{4}=1\frac{1}{4}\).

Ответ: а) \(\frac{11}{45}\); б) \(\frac{8}{35}\); в) \(\frac{9}{7}\); г) \(\frac{9}{7}\); д) \(\frac{19}{28}\); е) \(\frac{10}{9}\); ж) \(\frac{9}{10}\); з) \(\frac{5}{4}\).