2. Найди значение выражения (по действиям)

Решение:

а) \( \frac{3}{8} - \frac{2}{5} : \frac{1}{5} \)

1. \( \frac{2}{5} : \frac{1}{5} = \frac{2}{5} \times \frac{5}{1} = 2 \)
2. \( \frac{3}{8} - 2 = \frac{3}{8} - \frac{16}{8} = -\frac{13}{8} \)

б) \( \frac{2}{3} : \left( -\frac{1}{3} + \frac{2}{9} \right) \)

1. \( -\frac{1}{3} + \frac{2}{9} = -\frac{3}{9} + \frac{2}{9} = -\frac{1}{9} \)
2. \( \frac{2}{3} : \left( -\frac{1}{9} \right) = \frac{2}{3} \times (-9) = -6 \)

в) \( ( \frac{3}{5} - \frac{1}{3} ) : \frac{1}{20} \)

1. \( \frac{3}{5} - \frac{1}{3} = \frac{9}{15} - \frac{5}{15} = \frac{4}{15} \)
2. \( \frac{4}{15} : \frac{1}{20} = \frac{4}{15} \times 20 = \frac{4 \times 4}{3} = \frac{16}{3} \)

г) \( (\frac{1}{8} - \frac{3}{4}) : (\frac{1}{2} - \frac{7}{8}) \)

1. \( \frac{1}{8} - \frac{3}{4} = \frac{1}{8} - \frac{6}{8} = -\frac{5}{8} \)
2. \( \frac{1}{2} - \frac{7}{8} = \frac{4}{8} - \frac{7}{8} = -\frac{3}{8} \)
3. \( -\frac{5}{8} : (-\frac{3}{8}) = \frac{5}{8} \times \frac{8}{3} = \frac{5}{3} \)

д) \( -10 \frac{1}{3} + (\frac{2}{7} - \frac{5}{14}) \)

1. \( -10 \frac{1}{3} = -\frac{31}{3} \)
2. \( \frac{2}{7} - \frac{5}{14} = \frac{4}{14} - \frac{5}{14} = -\frac{1}{14} \)
3. \(-\frac{31}{3} - \frac{1}{14} = -\frac{31 \times 14}{42} - \frac{1 \times 3}{42} = -\frac{434}{42} - \frac{3}{42} = -\frac{437}{42} \)

е) \( -7 : 4 \frac{2}{3} - (3 \frac{1}{5} : 2) \)

1. \( -7 : \frac{14}{3} = -7 \times \frac{3}{14} = -\frac{3}{2} \)
2. \( 3 \frac{1}{5} = \frac{16}{5} \)
3. \( \frac{16}{5} : 2 = \frac{16}{5} \times \frac{1}{2} = \frac{8}{5} \)
4. \( -\frac{3}{2} - \frac{8}{5} = -\frac{15}{10} - \frac{16}{10} = -\frac{31}{10} \)

Ответ: а) \(-\frac{13}{8}\); б) -6; в) \(\frac{16}{3}\); г) \(\frac{5}{3}\); д) \(-\frac{437}{42}\); е) \(-\frac{31}{10}\).