Тема 2 «Смешанные числа» Найдите значение выражения (1-5): 1. 8-3\(\frac{2}{5}\) 2. -3:5\(\frac{1}{4}\)\(\frac{7}{8}\) 4. \(\frac{1}{6}\)-\(\frac{1}{2}-\frac{7}{18}\) 5*. 3\(\frac{2}{11}\)\(\6-\frac{13}{11}\)+13\(\frac{2}{11}\)\(\frac{3}{11}-6\).

Решение:

1. \(8 - 3\frac{2}{5} = 8 - \frac{17}{5} = \frac{40}{5} - \frac{17}{5} = \frac{23}{5} = 4\frac{3}{5}\)
2. \(-3 : 5\frac{1}{4} \cdot \frac{7}{8} = -3 : \frac{21}{4} \cdot \frac{7}{8} = -3 \cdot \frac{4}{21} \cdot \frac{7}{8} = -\frac{12}{21} \cdot \frac{7}{8} = -\frac{4}{7} \cdot \frac{7}{8} = -\frac{4}{8} = -\frac{1}{2}\)
3. \(\frac{1}{6} - (\frac{1}{2} - \frac{7}{18}) = \frac{1}{6} - (\frac{9}{18} - \frac{7}{18}) = \frac{1}{6} - \frac{2}{18} = \frac{1}{6} - \frac{1}{9} = \frac{3}{18} - \frac{2}{18} = \frac{1}{18}\)
4. \(3\frac{2}{11} \cdot (6 - \frac{13}{11}) + 13\frac{2}{11} \cdot (\frac{3}{11} - 6) = \frac{35}{11} \cdot (\frac{66}{11} - \frac{13}{11}) + \frac{145}{11} \cdot (\frac{3}{11} - \frac{66}{11}) = \frac{35}{11} \cdot \frac{53}{11} + \frac{145}{11} \cdot (-\frac{63}{11}) = \frac{1855}{121} - \frac{9135}{121} = -\frac{7280}{121}\)

Ответ: 1. \(4\frac{3}{5}\); 2. \(-\frac{1}{2}\); 3. \(\frac{1}{18}\); 4. \(-\frac{7280}{121}\).