1. Вычислите: a) \(\frac{2}{5}\cdot 1\frac{1}{4};\) б) \(2\frac{1}{9}\cdot 4;\) в) \(2\frac{1}{7}\cdot 1\frac{2}{5};\) г) \(1\frac{9}{11}:\frac{4}{5};\) д) \(17:1\frac{8}{9};\) е) \(1\frac{1}{14}:1\frac{2}{7}.\)

Решение:

1. a) \(\frac{2}{5}\cdot 1\frac{1}{4}=\frac{2}{5}\cdot \frac{5}{4}=\frac{2\cdot 5}{5\cdot 4}=\frac{1\cdot 1}{1\cdot 2}=\frac{1}{2}\)
2. б) \(2\frac{1}{9}\cdot 4 = \frac{19}{9}\cdot 4 = \frac{19\cdot 4}{9} = \frac{76}{9} = 8\frac{4}{9}\)
3. в) \(2\frac{1}{7}\cdot 1\frac{2}{5} = \frac{15}{7}\cdot \frac{7}{5} = \frac{15\cdot 7}{7\cdot 5} = \frac{3\cdot 1}{1\cdot 1} = 3\)
4. г) \(1\frac{9}{11}:\frac{4}{5} = \frac{20}{11}:\frac{4}{5} = \frac{20}{11}\cdot \frac{5}{4} = \frac{20\cdot 5}{11\cdot 4} = \frac{5\cdot 5}{11\cdot 1} = \frac{25}{11} = 2\frac{3}{11}\)
5. д) \(17:1\frac{8}{9} = 17:\frac{17}{9} = 17\cdot \frac{9}{17} = \frac{17\cdot 9}{17} = \frac{1\cdot 9}{1} = 9\)
6. е) \(1\frac{1}{14}:1\frac{2}{7} = \frac{15}{14}:\frac{9}{7} = \frac{15}{14}\cdot \frac{7}{9} = \frac{15\cdot 7}{14\cdot 9} = \frac{5\cdot 1}{2\cdot 3} = \frac{5}{6}\)

Ответ: a) \(\frac{1}{2}\); б) \(8\frac{4}{9}\); в) 3; г) \(2\frac{3}{11}\); д) 9; е) \(\frac{5}{6}\)