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}.

Ответ: a) -1 1/6; б) 2/3; в) -2 6/7; г) 2 2/3; д) -1/20; е) -11

Решаем:

a)

\[-\frac{7}{9} : \frac{2}{3} = -\frac{7}{9} \cdot \frac{3}{2} = -\frac{7 \cdot 3}{9 \cdot 2} = -\frac{7 \cdot 1}{3 \cdot 2} = -\frac{7}{6} = -1\frac{1}{6}\]

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)

\[\frac{16}{35} : (-\frac{4}{25}) = -\frac{16}{35} \cdot \frac{25}{4} = -\frac{16 \cdot 25}{35 \cdot 4} = -\frac{4 \cdot 5}{7 \cdot 1} = -\frac{20}{7} = -2\frac{6}{7}\]

г)

\[-\frac{5}{8} : (-\frac{15}{64}) = \frac{5}{8} \cdot \frac{64}{15} = \frac{5 \cdot 64}{8 \cdot 15} = \frac{1 \cdot 8}{1 \cdot 3} = \frac{8}{3} = 2\frac{2}{3}\]

д)

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

е)

\[-9 : \frac{9}{11} = -9 \cdot \frac{11}{9} = -\frac{9 \cdot 11}{9} = -11\]

Ответ: a) -1 1/6; б) 2/3; в) -2 6/7; г) 2 2/3; д) -1/20; е) -11