291. Выполните действия: 1) 7 7/9 - 4 1/12 + 2 5/18; 2) 17 2/3 - 6 1/4 + 3 5/6; 3) 10 9/16 - (3 11/12 + 4 4/9); 4) (20 - 7 23/36) - (14 4/27 - 6 1/18).

Решение:

1. \( 7 \frac{7}{9} - 4 \frac{1}{12} + 2 \frac{5}{18} = \frac{70}{9} - \frac{49}{12} + \frac{41}{18} = \frac{280}{36} - \frac{147}{36} + \frac{82}{36} = \frac{215}{36} = 5 \frac{35}{36} \)
2. \( 17 \frac{2}{3} - 6 \frac{1}{4} + 3 \frac{5}{6} = \frac{53}{3} - \frac{25}{4} + \frac{23}{6} = \frac{212}{12} - \frac{75}{12} + \frac{46}{12} = \frac{183}{12} = \frac{61}{4} = 15 \frac{1}{4} \)
3. \( 10 \frac{9}{16} - (3 \frac{11}{12} + 4 \frac{4}{9}) = \frac{169}{16} - (\frac{47}{12} + \frac{40}{9}) = \frac{169}{16} - (\frac{141}{36} + \frac{160}{36}) = \frac{169}{16} - \frac{301}{36} = \frac{1521}{144} - \frac{1204}{144} = \frac{317}{144} = 2 \frac{29}{144} \)
4. \( (20 - 7 \frac{23}{36}) - (14 \frac{4}{27} - 6 \frac{1}{18}) = (20 - \frac{275}{36}) - (\frac{382}{27} - \frac{109}{18}) = \frac{720 - 275}{36} - \frac{764 - 581}{54} = \frac{445}{36} - \frac{183}{54} = \frac{1335}{108} - \frac{366}{108} = \frac{969}{108} = \frac{107}{12} = 8 \frac{11}{12} \)

Ответ: 1) \( 5 \frac{35}{36} \); 2) \( 15 \frac{1}{4} \); 3) \( 2 \frac{29}{144} \); 4) \( 8 \frac{11}{12} \).