199. Найдите значение выражения: 1) \( \frac{7}{18} + \frac{11}{12} \) : \( \frac{19}{48} \); 2) \( \frac{7}{16} - \left( -\frac{5}{24} \right) \) : \( -1 \frac{5}{16} \); 3) \( \frac{10}{21} - \frac{25}{28} \) : \( \frac{11}{14} + \frac{24}{35} \); 4) \( -2 \frac{2}{3} + 2 \frac{1}{3} \) : \( -1 \frac{5}{7} - (-4,8) : \frac{4}{15} \).

Решение:

1. 1) \( \frac{7}{18} + \frac{11}{12} = \frac{14+33}{36} = \frac{47}{36} \)
   \( \frac{47}{36} : \frac{19}{48} = \frac{47}{36} \cdot \frac{48}{19} = \frac{47 \cdot 4}{3 \cdot 19} = \frac{188}{57} \)
2. 2) \( \frac{7}{16} - \left( -\frac{5}{24} \right) = \frac{7}{16} + \frac{5}{24} = \frac{21+10}{48} = \frac{31}{48} \)
   \( -1 \frac{5}{16} = -\frac{21}{16} \)
   \( \frac{31}{48} : \left(-\frac{21}{16}\right) = \frac{31}{48} \cdot \left(-\frac{16}{21}\right) = -\frac{31}{3 \cdot 21} = -\frac{31}{63} \)
3. 3) \( \frac{10}{21} - \frac{25}{28} = \frac{40-75}{84} = -\frac{35}{84} = -\frac{5}{12} \)
   \( \frac{11}{14} + \frac{24}{35} = \frac{55+48}{70} = \frac{103}{70} \)
   \( -\frac{5}{12} : \frac{103}{70} = -\frac{5}{12} \cdot \frac{70}{103} = -\frac{5 \cdot 35}{6 \cdot 103} = -\frac{175}{618} \)
4. 4) \( -2 \frac{2}{3} + 2 \frac{1}{3} = -\frac{8}{3} + \frac{7}{3} = -\frac{1}{3} \)
   \( -1 \frac{5}{7} = -\frac{12}{7} \)
   \( -4,8 = -4 \frac{4}{5} = -\frac{24}{5} \)
   \( -4,8 : \frac{4}{15} = -\frac{24}{5} : \frac{4}{15} = -\frac{24}{5} \cdot \frac{15}{4} = -6 \cdot 3 = -18 \)
   \( -1 \frac{5}{7} - (-18) = -\frac{12}{7} + 18 = \frac{-12+126}{7} = \frac{114}{7} \)
   \( -\frac{1}{3} : \frac{114}{7} = -\frac{1}{3} \cdot \frac{7}{114} = -\frac{7}{342} \)

Ответ: 1) \( \frac{188}{57} \); 2) \( -\frac{31}{63} \); 3) \( -\frac{175}{618} \); 4) \( -\frac{7}{342} \).