§5. Обыкновенные дроби — Упражнения — 5.414 — стр. 68

\( \frac{23}{30} - \left( \frac{1}{6} + \frac{2}{5} \right) \)

\( \frac{1}{6} = \frac{5}{30}, \quad \frac{2}{5} = \frac{12}{30}. \)

Тогда:

\( \frac{23}{30} - \left( \frac{5}{30} + \frac{12}{30} \right) = \frac{23}{30} - \frac{17}{30} = \frac{6}{30} = \frac{1}{5} \).

\( \frac{11}{42} + \left( \frac{3}{7} - \frac{1}{6} \right) \)

\( \frac{3}{7} = \frac{18}{42}, \quad \frac{1}{6} = \frac{7}{42}. \)

Тогда:

\( \frac{11}{42} + \left( \frac{18}{42} - \frac{7}{42} \right) = \frac{11}{42} + \frac{11}{42} = \frac{22}{42} = \frac{11}{21} \).

\( \frac{11}{15} - \left( \frac{2}{3} - \frac{3}{5} \right) \)

\( \frac{2}{3} = \frac{10}{15}, \quad \frac{3}{5} = \frac{9}{15}. \)

Тогда:

\( \frac{11}{15} - \left( \frac{10}{15} - \frac{9}{15} \right) = \frac{11}{15} - \frac{1}{15} = \frac{10}{15} = \frac{2}{3} \).

\( \frac{5}{18} + \left( \frac{2}{9} + \frac{1}{2} \right) \)

\( \frac{2}{9} = \frac{4}{18}, \quad \frac{1}{2} = \frac{9}{18}. \)

Тогда:

\( \frac{5}{18} + \left( \frac{4}{18} + \frac{9}{18} \right) = \frac{5}{18} + \frac{13}{18} = \frac{18}{18} = 1 \).