E) \(\frac{27\frac{3}{8}-21\frac{7}{20}}{3\frac{4}{7}-1\frac{23}{28}-(1\frac{47}{65}-\frac{29}{130})}\)

Решение:

Числитель:

1. \( 27\frac{3}{8} = \frac{27\cdot8+3}{8} = \frac{216+3}{8} = \frac{219}{8} \)
2. \( 21\frac{7}{20} = \frac{21\cdot20+7}{20} = \frac{420+7}{20} = \frac{427}{20} \)
3. \( \frac{219}{8} - \frac{427}{20} = \frac{219\cdot5 - 427\cdot2}{40} = \frac{1095 - 854}{40} = \frac{241}{40} \)

Знаменатель:

1. \( 3\frac{4}{7} = \frac{3\cdot7+4}{7} = \frac{21+4}{7} = \frac{25}{7} \)
2. \( 1\frac{23}{28} = \frac{1\cdot28+23}{28} = \frac{28+23}{28} = \frac{51}{28} \)
3. \( 1\frac{47}{65} = \frac{1\cdot65+47}{65} = \frac{65+47}{65} = \frac{112}{65} \)
4. \( \frac{112}{65} - \frac{29}{130} = \frac{112\cdot2 - 29}{130} = \frac{224 - 29}{130} = \frac{195}{130} = \frac{3}{2} \)
5. \( \frac{25}{7} - \frac{51}{28} - \frac{3}{2} = \frac{25\cdot4 - 51 - 3\cdot14}{28} = \frac{100 - 51 - 42}{28} = \frac{7}{28} = \frac{1}{4} \)

Делим числитель на знаменатель:

1. \( \frac{241}{40} : \frac{1}{4} = \frac{241}{40} \cdot 4 = \frac{241}{10} \)

Ответ: \(\frac{241}{10}\)