4.310 Выполните деление: a) \(3\frac{5}{9}:(-\frac{4}{27})\); б) \(-4\frac{1}{8}:(-33)\); в) \(-1\frac{3}{11}:(-3\frac{7}{22})\); г) \(-7\frac{1}{7}:1\frac{11}{49}\).

Ответ:

1. a) \(3\frac{5}{9}:(-\frac{4}{27}) = \frac{32}{9} : (-\frac{4}{27}) = \frac{32}{9} \cdot (-\frac{27}{4}) = -\frac{32 \cdot 27}{9 \cdot 4} = -\frac{8 \cdot 3}{1 \cdot 1} = -24\)

2. б) \(-4\frac{1}{8}:(-33) = -\frac{33}{8} : (-33) = -\frac{33}{8} \cdot (-\frac{1}{33}) = \frac{33 \cdot 1}{8 \cdot 33} = \frac{1}{8}\)

3. в) \(-1\frac{3}{11}:(-3\frac{7}{22}) = -\frac{14}{11} : (-\frac{73}{22}) = -\frac{14}{11} \cdot (-\frac{22}{73}) = \frac{14 \cdot 22}{11 \cdot 73} = \frac{2 \cdot 2}{1 \cdot 1} = \frac{4}{1}\)

4. г) \(-7\frac{1}{7}:1\frac{11}{49}) = -\frac{50}{7} : \frac{60}{49} = -\frac{50}{7} \cdot \frac{49}{60} = -\frac{50 \cdot 49}{7 \cdot 60} = -\frac{5 \cdot 7}{1 \cdot 6} = -\frac{35}{6} = -5\frac{5}{6}\)

Ответ: