199. Найдите значение выражения: 1) (4/15 + 7/12) * (-38/45); 2) (11/16 - 17/24) : (-5/12); 3) (-11/18 + 29/45) : (35/54 - 19/27); 4) -4(1/7) + 2(1/4) * (-11(2/9) - (-5,4) : 9/35).

Решение:

1. \( \left( \frac{4}{15} + \frac{7}{12} \right) \cdot \left( -\frac{38}{45} \right) = \left( \frac{16+35}{60} \right) \cdot \left( -\frac{38}{45} \right) = \frac{51}{60} \cdot \left( -\frac{38}{45} \right) = \frac{17}{20} \cdot \left( -\frac{38}{45} \right) = \frac{17}{10} \cdot \left( -\frac{19}{45} \right) = -\frac{323}{450} \)
2. \( \left( \frac{11}{16} - \frac{17}{24} \right) : \left( -\frac{5}{12} \right) = \left( \frac{33-34}{48} \right) : \left( -\frac{5}{12} \right) = \frac{-1}{48} : \left( -\frac{5}{12} \right) = \frac{1}{48} \cdot \frac{12}{5} = \frac{1}{4} \cdot \frac{1}{5} = \frac{1}{20} \)
3. \( \left( -\frac{11}{18} + \frac{29}{45} \right) : \left( \frac{35}{54} - \frac{19}{27} \right) = \left( \frac{-55+58}{90} \right) : \left( \frac{35-38}{54} \right) = \frac{3}{90} : \frac{-3}{54} = \frac{1}{30} : \frac{-3}{54} = \frac{1}{30} \cdot \left( -\frac{54}{3} \right) = \frac{1}{30} \cdot \left( -18 \right) = -\frac{18}{30} = -\frac{3}{5} \)
4. \( -4\frac{1}{7} + 2\frac{1}{4} \cdot \left( -11\frac{2}{9} - (-5,4) : \frac{9}{35} \right) = -\frac{29}{7} + \frac{9}{4} \cdot \left( -\frac{101}{9} - (-5\frac{4}{10}) : \frac{9}{35} \right) = -\frac{29}{7} + \frac{9}{4} \cdot \left( -\frac{101}{9} - (-5\frac{2}{5}) : \frac{9}{35} \right) = -\frac{29}{7} + \frac{9}{4} \cdot \left( -\frac{101}{9} - \left( -\frac{27}{5} \right) : \frac{9}{35} \right) = -\frac{29}{7} + \frac{9}{4} \cdot \left( -\frac{101}{9} - \left( -\frac{27}{5} \right) \cdot \frac{35}{9} \right) = -\frac{29}{7} + \frac{9}{4} \cdot \left( -\frac{101}{9} - \left( -3 \right) \cdot 7 \right) = -\frac{29}{7} + \frac{9}{4} \cdot \left( -\frac{101}{9} + 21 \right) = -\frac{29}{7} + \frac{9}{4} \cdot \left( \frac{-101+189}{9} \right) = -\frac{29}{7} + \frac{9}{4} \cdot \frac{88}{9} = -\frac{29}{7} + \frac{88}{4} = -\frac{29}{7} + 22 = \frac{-29+154}{7} = \frac{125}{7} = 17\frac{6}{7} \)

Ответ: 1) -323/450; 2) 1/20; 3) -3/5; 4) 17 6/7.