5.414 Найдите значение выражения:

Решение:

1. \( \frac{23}{30} - (\frac{1}{6} + \frac{2}{5}) = \frac{23}{30} - (\frac{5}{30} + \frac{12}{30}) = \frac{23}{30} - \frac{17}{30} = \frac{6}{30} = \frac{1}{5} \)
2. \( \frac{11}{42} + (\frac{3}{7} - \frac{1}{6}) = \frac{11}{42} + (\frac{18}{42} - \frac{7}{42}) = \frac{11}{42} + \frac{11}{42} = \frac{22}{42} = \frac{11}{21} \)
3. \( \frac{11}{15} - (\frac{2}{3} - \frac{3}{5}) = \frac{11}{15} - (\frac{10}{15} - \frac{9}{15}) = \frac{11}{15} - \frac{1}{15} = \frac{10}{15} = \frac{2}{3} \)
4. \( \frac{3}{7} + \frac{9}{14} - \frac{2}{21} = \frac{18}{42} + \frac{27}{42} - \frac{4}{42} = \frac{45}{42} - \frac{4}{42} = \frac{41}{42} \)
5. \( 2\frac{1}{3} + \frac{1}{5} - 1\frac{1}{8} = \frac{7}{3} + \frac{1}{5} - \frac{9}{8} = \frac{280}{120} + \frac{24}{120} - \frac{135}{120} = \frac{304}{120} - \frac{135}{120} = \frac{169}{120} = 1\frac{49}{120} \)
6. \( \frac{5}{18} + (\frac{2}{9} \div \frac{1}{2}) = \frac{5}{18} + (\frac{2}{9} \times 2) = \frac{5}{18} + \frac{4}{9} = \frac{5}{18} + \frac{8}{18} = \frac{13}{18} \)

Ответ: a) \( \frac{1}{5} \), б) \( \frac{11}{21} \), в) \( \frac{2}{3} \), г) \( \frac{41}{42} \), д) \( 1\frac{49}{120} \), г) \( \frac{13}{18} \).