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

1. a) \[-\frac{7}{9} : \frac{2}{3} = -\frac{7}{9} \cdot \frac{3}{2} = -\frac{7 \cdot 3}{9 \cdot 2} = -\frac{7 \cdot \cancel{3}}{3 \cdot \cancel{3} \cdot 2} = -\frac{7}{3 \cdot 2} = -\frac{7}{6} = -1\frac{1}{6}\]
2. б) \[-\frac{3}{13} :(-\frac{9}{26}) = \frac{3}{13} : \frac{9}{26} = \frac{3}{13} \cdot \frac{26}{9} = \frac{3 \cdot 26}{13 \cdot 9} = \frac{\cancel{3} \cdot 2 \cdot \cancel{13}}{\cancel{13} \cdot 3 \cdot \cancel{3}} = \frac{2}{3}\]
3. в) \[\frac{16}{35}:(-\frac{4}{25}) = -(\frac{16}{35}:\frac{4}{25}) = -(\frac{16}{35} \cdot \frac{25}{4}) = -\frac{16 \cdot 25}{35 \cdot 4} = -\frac{4 \cdot \cancel{4} \cdot 5 \cdot \cancel{5}}{7 \cdot \cancel{5} \cdot \cancel{4}} = -\frac{4 \cdot 5}{7} = -\frac{20}{7} = -2\frac{6}{7}\]
4. г) \[-\frac{5}{8} :(-\frac{15}{64}) = \frac{5}{8} : \frac{15}{64} = \frac{5}{8} \cdot \frac{64}{15} = \frac{5 \cdot 64}{8 \cdot 15} = \frac{\cancel{5} \cdot 8 \cdot \cancel{8}}{\cancel{8} \cdot 3 \cdot \cancel{5}} = \frac{8}{3} = 2\frac{2}{3}\]
5. д) \[ \frac{4}{5} : (-16) = -(\frac{4}{5} : 16) = -(\frac{4}{5} \cdot \frac{1}{16}) = -\frac{4 \cdot 1}{5 \cdot 16} = -\frac{\cancel{4}}{5 \cdot 4 \cdot \cancel{4}} = -\frac{1}{5 \cdot 4} = -\frac{1}{20}\]
6. е) \[-9 : \frac{9}{11} = -9 \cdot \frac{11}{9} = -\frac{9 \cdot 11}{9} = -\frac{\cancel{9} \cdot 11}{\cancel{9}} = -11\]

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