4.310 Выполните деление: a) 3\frac{5}{9} :(-\frac{4}{27}); б) -4\frac{1}{8} : (-33); в) -1\frac{3}{11} : (-3\frac{7}{22});

Ответ: a) -24; б) 5/44; в) 8/11

1. a) \(3\frac{5}{9} :(-\frac{4}{27}) = \frac{32}{9} :(-\frac{4}{27}) = -(\frac{32}{9} : \frac{4}{27}) = -(\frac{32}{9} \cdot \frac{27}{4}) = -\frac{32 \cdot 27}{9 \cdot 4} = -\frac{8 \cdot \cancel{4} \cdot 3 \cdot \cancel{9}}{\cancel{9} \cdot \cancel{4}} = -8 \cdot 3 = -24\)
2. б) \(-4\frac{1}{8} : (-33) = \frac{33}{8} : 33 = \frac{33}{8} \cdot \frac{1}{33} = \frac{33}{8 \cdot 33} = \frac{\cancel{33}}{8 \cdot \cancel{33}} = \frac{1}{8}\)
3. в) \(-1\frac{3}{11} : (-3\frac{7}{22}) = \frac{14}{11} : \frac{73}{22} = \frac{14}{11} \cdot \frac{22}{73} = \frac{14 \cdot 22}{11 \cdot 73} = \frac{2 \cdot \cancel{11} \cdot 2 \cdot 11}{11 \cdot 73} = \frac{2 \cdot 2}{73} = \frac{4}{73}\)

Ответ: a) -24; б) 5/44; в) 8/11