1. \(\frac{3}{4}-(\frac{1}{2}+\frac{1}{8})+\frac{2}{5}\) 2. \(\frac{2}{3} \cdot \frac{5}{6} + \frac{3}{10} - \frac{1}{15}\) 3. \((\frac{7}{9} - \frac{1}{3}) : \frac{2}{9} + \frac{1}{4}\) 4. \(\frac{3}{5} + \frac{4}{7} \cdot (\frac{1}{2} - \frac{1}{14})\) 5. \((\frac{5}{6} : \frac{1}{3}) - (\frac{2}{5} + \frac{1}{10})\)

Решение:

1. \(\frac{3}{4}-(\frac{1}{2}+\frac{1}{8})+\frac{2}{5} = \frac{3}{4}-(\frac{4}{8}+\frac{1}{8})+\frac{2}{5} = \frac{3}{4}-\frac{5}{8}+\frac{2}{5} = \frac{30}{40}-\frac{25}{40}+\frac{16}{40} = \frac{30-25+16}{40} = \frac{21}{40}\)
   Ответ: \(\frac{21}{40}\)
2. \(\frac{2}{3} \cdot \frac{5}{6} + \frac{3}{10} - \frac{1}{15} = \frac{2 \cdot 5}{3 \cdot 6} + \frac{3}{10} - \frac{1}{15} = \frac{10}{18} + \frac{3}{10} - \frac{1}{15} = \frac{5}{9} + \frac{3}{10} - \frac{1}{15} = \frac{50}{90} + \frac{27}{90} - \frac{6}{90} = \frac{50 + 27 - 6}{90} = \frac{71}{90}\)
   Ответ: \(\frac{71}{90}\)
3. \((\frac{7}{9} - \frac{1}{3}) : \frac{2}{9} + \frac{1}{4} = (\frac{7}{9} - \frac{3}{9}) : \frac{2}{9} + \frac{1}{4} = \frac{4}{9} : \frac{2}{9} + \frac{1}{4} = \frac{4}{9} \cdot \frac{9}{2} + \frac{1}{4} = \frac{4 \cdot 9}{9 \cdot 2} + \frac{1}{4} = \frac{36}{18} + \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}\)
   Ответ: \(\frac{9}{4}\)
4. \(\frac{3}{5} + \frac{4}{7} \cdot (\frac{1}{2} - \frac{1}{14}) = \frac{3}{5} + \frac{4}{7} \cdot (\frac{7}{14} - \frac{1}{14}) = \frac{3}{5} + \frac{4}{7} \cdot \frac{6}{14} = \frac{3}{5} + \frac{4}{7} \cdot \frac{3}{7} = \frac{3}{5} + \frac{4 \cdot 3}{7 \cdot 7} = \frac{3}{5} + \frac{12}{49} = \frac{147}{245} + \frac{60}{245} = \frac{147 + 60}{245} = \frac{207}{245}\)
   Ответ: \(\frac{207}{245}\)
5. \((\frac{5}{6} : \frac{1}{3}) - (\frac{2}{5} + \frac{1}{10}) = (\frac{5}{6} \cdot \frac{3}{1}) - (\frac{4}{10} + \frac{1}{10}) = \frac{5 \cdot 3}{6 \cdot 1} - \frac{5}{10} = \frac{15}{6} - \frac{1}{2} = \frac{5}{2} - \frac{1}{2} = \frac{5 - 1}{2} = \frac{4}{2} = 2\)
   Ответ: 2