5.535 Выполните действия: a) \(\frac{1}{3} : \frac{3}{7} : \frac{1}{6}\) b) \(\frac{1}{18} : \frac{3}{5} : \frac{1}{3}\) c) \(\frac{1}{3} : \frac{3}{4} : \frac{1}{4}\) d) \(\frac{2}{3} : \frac{6}{11}\) e) \((\frac{1}{5} + \frac{1}{20}) : \frac{4}{5}\) f) \((\frac{1}{3} - \frac{1}{4}) : 12\)

**a) \(\frac{1}{3} : \frac{3}{7} : \frac{1}{6}\)** 1. \(\frac{1}{3} : \frac{3}{7} = \frac{1}{3} \cdot \frac{7}{3} = \frac{7}{9}\) 2. \(\frac{7}{9} : \frac{1}{6} = \frac{7}{9} \cdot \frac{6}{1} = \frac{42}{9} = \frac{14}{3}\) **Ответ: \(\frac{14}{3}\)** **b) \(\frac{1}{18} : \frac{3}{5} : \frac{1}{3}\)** 1. \(\frac{1}{18} : \frac{3}{5} = \frac{1}{18} \cdot \frac{5}{3} = \frac{5}{54}\) 2. \(\frac{5}{54} : \frac{1}{3} = \frac{5}{54} \cdot \frac{3}{1} = \frac{15}{54} = \frac{5}{18}\) **Ответ: \(\frac{5}{18}\)** **c) \(\frac{1}{3} : \frac{3}{4} : \frac{1}{4}\)** 1. \(\frac{1}{3} : \frac{3}{4} = \frac{1}{3} \cdot \frac{4}{3} = \frac{4}{9}\) 2. \(\frac{4}{9} : \frac{1}{4} = \frac{4}{9} \cdot \frac{4}{1} = \frac{16}{9}\) **Ответ: \(\frac{16}{9}\)** **d) \(\frac{2}{3} : \frac{6}{11}\)** \[\frac{2}{3} : \frac{6}{11} = \frac{2}{3} \cdot \frac{11}{6} = \frac{22}{18} = \frac{11}{9}\] **Ответ: \(\frac{11}{9}\)** **e) \((\frac{1}{5} + \frac{1}{20}) : \frac{4}{5}\)** 1. \(\frac{1}{5} + \frac{1}{20} = \frac{4}{20} + \frac{1}{20} = \frac{5}{20} = \frac{1}{4}\) 2. \(\frac{1}{4} : \frac{4}{5} = \frac{1}{4} \cdot \frac{5}{4} = \frac{5}{16}\) **Ответ: \(\frac{5}{16}\)** **f) \((\frac{1}{3} - \frac{1}{4}) : 12\)** 1. \(\frac{1}{3} - \frac{1}{4} = \frac{4}{12} - \frac{3}{12} = \frac{1}{12}\) 2. \(\frac{1}{12} : 12 = \frac{1}{12} \cdot \frac{1}{12} = \frac{1}{144}\) **Ответ: \(\frac{1}{144}\)**