1. Выполните действия: 1) (1,8 + 1 2/7) : (1,8 - 1 2/7); 2) (1,5 + 1 1/3) : (7,6 - 5 1/3); 3) (23 - 15 1/3) : (-5 1/9); 4) (19 - 13 2/3) : (-7 1/9).

Решение:

1. 1) \( \left( 1.8 + 1 \frac{2}{7} \right) : \left( 1.8 - 1 \frac{2}{7} \right) \)
   \( 1.8 = \frac{18}{10} = \frac{9}{5} \)
   \( 1 \frac{2}{7} = \frac{9}{7} \)
   \( \frac{9}{5} + \frac{9}{7} = \frac{63 + 45}{35} = \frac{108}{35} \)
   \( \frac{9}{5} - \frac{9}{7} = \frac{63 - 45}{35} = \frac{18}{35} \)
   \( \frac{108}{35} : \frac{18}{35} = \frac{108}{35} \cdot \frac{35}{18} = \frac{108}{18} = 6 \)
2. 2) \( \left( 1.5 + 1 \frac{1}{3} \right) : \left( 7.6 - 5 \frac{1}{3} \right) \)
   \( 1.5 = \frac{3}{2} \)
   \( 1 \frac{1}{3} = \frac{4}{3} \)
   \( \frac{3}{2} + \frac{4}{3} = \frac{9 + 8}{6} = \frac{17}{6} \)
   \( 7.6 = \frac{76}{10} = \frac{38}{5} \)
   \( 5 \frac{1}{3} = \frac{16}{3} \)
   \( \frac{38}{5} - \frac{16}{3} = \frac{114 - 80}{15} = \frac{34}{15} \)
   \( \frac{17}{6} : \frac{34}{15} = \frac{17}{6} \cdot \frac{15}{34} = \frac{1}{2} \cdot \frac{5}{2} = \frac{5}{4} = 1.25 \)
3. 3) \( \left( 23 - 15 \frac{1}{3} \right) : \left( -5 \frac{1}{9} \right) \)
   \( 23 - 15 \frac{1}{3} = 22 \frac{3}{3} - 15 \frac{1}{3} = 7 \frac{2}{3} = \frac{23}{3} \)
   \( -5 \frac{1}{9} = - \frac{46}{9} \)
   \( \frac{23}{3} : \left( - \frac{46}{9} \right) = \frac{23}{3} \cdot \left( - \frac{9}{46} \right) = \frac{1}{1} \cdot \left( - \frac{3}{2} \right) = - \frac{3}{2} = -1.5 \)
4. 4) \( \left( 19 - 13 \frac{2}{3} \right) : \left( -7 \frac{1}{9} \right) \)
   \( 19 - 13 \frac{2}{3} = 18 \frac{3}{3} - 13 \frac{2}{3} = 5 \frac{1}{3} = \frac{16}{3} \)
   \( -7 \frac{1}{9} = - \frac{64}{9} \)
   \( \frac{16}{3} : \left( - \frac{64}{9} \right) = \frac{16}{3} \cdot \left( - \frac{9}{64} \right) = \frac{1}{1} \cdot \left( - \frac{3}{4} \right) = - \frac{3}{4} = -0.75 \)

Ответ: 1) 6; 2) 1.25; 3) -1.5; 4) -0.75.