1) (1,8 + 1\frac{2}{7}): (1,8-1\frac{2}{7}); 2) (1,5 + 1\frac{1}{3}): (7,6 - 5\frac{1}{3}); 3) (23-15\frac{1}{3}) : (-5\frac{1}{9}); 4) (19-13\frac{2}{3}): (-7\frac{1}{9}).

Выполните действия:

1. \( (1,8 + 1\frac{2}{7}): (1,8-1\frac{2}{7}) \)
   \( 1,8 = \frac{18}{10} = \frac{9}{5} \)
   \( 1\frac{2}{7} = \frac{9}{7} \)
   \( (\frac{9}{5} + \frac{9}{7}) : (\frac{9}{5} - \frac{9}{7}) = \frac{9}{5} + \frac{9}{7} = \frac{9*7 + 9*5}{35} = \frac{63 + 45}{35} = \frac{108}{35} \)
   \( \frac{9}{5} - \frac{9}{7} = \frac{9*7 - 9*5}{35} = \frac{63 - 45}{35} = \frac{18}{35} \)
   \( \frac{108}{35} : \frac{18}{35} = \frac{108}{35} * \frac{35}{18} = \frac{108}{18} = 6 \)

   Ответ: 6

2. \( (1,5 + 1\frac{1}{3}): (7,6 - 5\frac{1}{3}) \)
   \( 1,5 = \frac{15}{10} = \frac{3}{2} \)
   \( 1\frac{1}{3} = \frac{4}{3} \)
   \( 7,6 = \frac{76}{10} = \frac{38}{5} \)
   \( 5\frac{1}{3} = \frac{16}{3} \)
   \( (\frac{3}{2} + \frac{4}{3}) : (\frac{38}{5} - \frac{16}{3}) = \frac{3}{2} + \frac{4}{3} = \frac{3*3 + 4*2}{6} = \frac{9 + 8}{6} = \frac{17}{6} \)
   \( \frac{38}{5} - \frac{16}{3} = \frac{38*3 - 16*5}{15} = \frac{114 - 80}{15} = \frac{34}{15} \)
   \( \frac{17}{6} : \frac{34}{15} = \frac{17}{6} * \frac{15}{34} = \frac{15}{6*2} = \frac{15}{12} = \frac{5}{4} = 1\frac{1}{4} \)

   Ответ: 1\frac{1}{4}

3. \( (23-15\frac{1}{3}) : (-5\frac{1}{9}) \)
   \( 15\frac{1}{3} = \frac{46}{3} \)
   \( 5\frac{1}{9} = \frac{46}{9} \)
   \( (23 - \frac{46}{3}) : (-\frac{46}{9}) = (\frac{23*3 - 46}{3}) : (-\frac{46}{9}) = \frac{23}{3} : (-\frac{46}{9}) = \frac{23}{3} * -\frac{9}{46} = -\frac{9}{3*2} = -\frac{3}{2} = -1\frac{1}{2} \)

   Ответ: -1\frac{1}{2}

4. \( (19-13\frac{2}{3}): (-7\frac{1}{9}) \)
   \( 13\frac{2}{3} = \frac{41}{3} \)
   \( 7\frac{1}{9} = \frac{64}{9} \)
   \( (19 - \frac{41}{3}) : (-\frac{64}{9}) = (\frac{19*3 - 41}{3}) : (-\frac{64}{9}) = \frac{16}{3} : (-\frac{64}{9}) = \frac{16}{3} * -\frac{9}{64} = -\frac{9}{3*4} = -\frac{3}{4} \)

   Ответ: -\frac{3}{4}