Деление дробей: решаем примеры

Деление дробей. Вычислите: 1. \(\frac{3}{4} : \frac{2}{5} = \frac{3}{4} \cdot \frac{5}{2} = \frac{3 \cdot 5}{4 \cdot 2} = \frac{15}{8} = 1\frac{7}{8}\) 2. \(-\frac{7}{9} : \frac{14}{3} = -\frac{7}{9} \cdot \frac{3}{14} = -\frac{7 \cdot 3}{9 \cdot 14} = -\frac{1 \cdot 1}{3 \cdot 2} = -\frac{1}{6}\) 3. \(\frac{5}{6} : 10 = \frac{5}{6} \cdot \frac{1}{10} = \frac{5 \cdot 1}{6 \cdot 10} = \frac{1 \cdot 1}{6 \cdot 2} = \frac{1}{12}\) 4. \(1,2 : \frac{3}{5} = \frac{12}{10} : \frac{3}{5} = \frac{6}{5} \cdot \frac{5}{3} = \frac{6 \cdot 5}{5 \cdot 3} = \frac{2 \cdot 1}{1 \cdot 1} = 2\) 5. \(-\frac{8}{3} : (-\frac{4}{9}) = \frac{8}{3} \cdot \frac{9}{4} = \frac{8 \cdot 9}{3 \cdot 4} = \frac{2 \cdot 3}{1 \cdot 1} = 6\) 6. \(\frac{11}{4} : \frac{22}{3} = \frac{11}{4} \cdot \frac{3}{22} = \frac{11 \cdot 3}{4 \cdot 22} = \frac{1 \cdot 3}{4 \cdot 2} = \frac{3}{8}\) 7. \(0,75 : \frac{3}{2} = \frac{75}{100} : \frac{3}{2} = \frac{3}{4} \cdot \frac{2}{3} = \frac{3 \cdot 2}{4 \cdot 3} = \frac{1 \cdot 1}{2 \cdot 1} = \frac{1}{2} = 0,5\) 8. \(-2,5 : \frac{5}{4} = -\frac{25}{10} : \frac{5}{4} = -\frac{5}{2} \cdot \frac{4}{5} = -\frac{5 \cdot 4}{2 \cdot 5} = -\frac{1 \cdot 2}{1 \cdot 1} = -2\) 9. \(0,(6) : \frac{2}{3} = \frac{6}{9} : \frac{2}{3} = \frac{2}{3} \cdot \frac{3}{2} = 1\) 10. \(\frac{9}{10} : (-0,3) = \frac{9}{10} : (-\frac{3}{10}) = -\frac{9}{10} \cdot \frac{10}{3} = -\frac{9 \cdot 10}{10 \cdot 3} = -3\)