4.309 Найдите частное: a) \(\frac{7}{9}:\frac{2}{3}\); б) \(-\frac{3}{13}:(-\frac{9}{26})\); в) \(\frac{16}{35}:(-\frac{4}{25})\); г) \(-\frac{5}{8}:(-\frac{15}{64})\); д) \(\frac{4}{5}:(-16)\); e) \(-9:\frac{9}{11}\).

а) \(\frac{7}{9}:\frac{2}{3} = \frac{7}{9} \cdot \frac{3}{2} = \frac{7 \cdot 3}{9 \cdot 2} = \frac{7 \cdot 1}{3 \cdot 2} = \frac{7}{6}\)

б) \(-\frac{3}{13}:(-\frac{9}{26}) = \frac{3}{13} \cdot \frac{26}{9} = \frac{3 \cdot 26}{13 \cdot 9} = \frac{1 \cdot 2}{1 \cdot 3} = \frac{2}{3}\)

в) \(\frac{16}{35}:(-\frac{4}{25}) = -(\frac{16}{35} \cdot \frac{25}{4}) = -(\frac{16 \cdot 25}{35 \cdot 4}) = -(\frac{4 \cdot 5}{7 \cdot 1}) = -\frac{20}{7}\)

г) \(-\frac{5}{8}:(-\frac{15}{64}) = \frac{5}{8} \cdot \frac{64}{15} = \frac{5 \cdot 64}{8 \cdot 15} = \frac{1 \cdot 8}{1 \cdot 3} = \frac{8}{3}\)

д) \(\frac{4}{5}:(-16) = -(\frac{4}{5}:16) = -\frac{4}{5} \cdot \frac{1}{16} = -(\frac{4 \cdot 1}{5 \cdot 16}) = -(\frac{1 \cdot 1}{5 \cdot 4}) = -\frac{1}{20}\)

е) \(-9:\frac{9}{11} = -9 \cdot \frac{11}{9} = -\frac{9 \cdot 11}{9} = -11\)