Выполните действия: 1) (1,8 + 11⁲⁄₇) : (1,8 - 11⁲⁄₇); 2) (1,5 + 11⁄₃) : (7,6 - 51⁄₃); 3) (23 - 151⁄₃) : (-51⁄₉); 4) (19 - 132⁄₃) : (-71⁄₉).

Решение:

1. \( 1,8 + 1\frac{2}{7} = \frac{18}{10} + \frac{9}{7} = \frac{9}{5} + \frac{9}{7} = \frac{63 + 45}{35} = \frac{108}{35} \)
2. \( 1,8 - 1\frac{2}{7} = \frac{9}{5} - \frac{9}{7} = \frac{63 - 45}{35} = \frac{18}{35} \)
3. \( \frac{108}{35} : \frac{18}{35} = \frac{108}{35} \cdot \frac{35}{18} = \frac{108}{18} = 6 \)
4. \( 1,5 + 1\frac{1}{3} = \frac{3}{2} + \frac{4}{3} = \frac{9 + 8}{6} = \frac{17}{6} \)
5. \( 7,6 - 5\frac{1}{3} = \frac{76}{10} - \frac{16}{3} = \frac{38}{5} - \frac{16}{3} = \frac{114 - 80}{15} = \frac{34}{15} \)
6. \( \frac{17}{6} : \frac{34}{15} = \frac{17}{6} \cdot \frac{15}{34} = \frac{1}{2} \cdot \frac{5}{2} = \frac{5}{4} \)
7. \( 23 - 15\frac{1}{3} = 23 - \frac{46}{3} = \frac{69 - 46}{3} = \frac{23}{3} \)
8. \( -5\frac{1}{9} = -\frac{46}{9} \)
9. \( \frac{23}{3} : \left(-\frac{46}{9}\right) = \frac{23}{3} \cdot \left(-\frac{9}{46}\right) = \frac{1}{1} \cdot \left(-\frac{3}{2}\right) = -\frac{3}{2} \)
10. \( 19 - 13\frac{2}{3} = 19 - \frac{41}{3} = \frac{57 - 41}{3} = \frac{16}{3} \)
11. \( -7\frac{1}{9} = -\frac{64}{9} \)
12. \( \frac{16}{3} : \left(-\frac{64}{9}\right) = \frac{16}{3} \cdot \left(-\frac{9}{64}\right) = \frac{1}{1} \cdot \left(-\frac{3}{4}\right) = -\frac{3}{4} \)

Ответ: 1) 6; 2) 1⁵⁄₄; 3) -1⁵⁄₂; 4) -3⁄₄.