Вопрос:

1. Найдите значение выражения: 1) \(81\frac{11}{30}-(32\frac{5}{8}+4\frac{1}{8})\); 2) \(\left(7\frac{8}{9}-5\frac{5}{6}\right)-1\frac{7}{18}\); 3) \(\left(65\frac{22}{35}-49\frac{2}{7}\right)-\left(57\frac{3}{5}-41\frac{9}{10}\right)\); 4) \(19\frac{11}{28}-\left(8\frac{3}{4}+10\frac{1}{7}\right)\).

Ответ:

  1. \(32\frac{5}{8}+4\frac{1}{8}=36\frac{6}{8}=36\frac{3}{4}\).
    \(81\frac{11}{30}-36\frac{3}{4}=81\frac{22}{60}-36\frac{45}{60}=44\frac{37}{60}\).
  2. \(7\frac{8}{9}-5\frac{5}{6}=7\frac{16}{18}-5\frac{15}{18}=2\frac{1}{18}\).
    \(2\frac{1}{18}-1\frac{7}{18}=\frac{29}{18}-\frac{25}{18}=\frac{4}{18}=\frac{2}{9}\).
  3. \(65\frac{22}{35}-49\frac{2}{7}=65\frac{22}{35}-49\frac{10}{35}=16\frac{12}{35}\).
    \(57\frac{3}{5}-41\frac{9}{10}=57\frac{6}{10}-41\frac{9}{10}=15\frac{7}{10}\).
    \(16\frac{12}{35}-15\frac{7}{10}=16\frac{24}{70}-15\frac{49}{70}=\frac{45}{70}=\frac{9}{14}\).
  4. \(8\frac{3}{4}+10\frac{1}{7}=18+\frac{21}{28}+\frac{4}{28}=18\frac{25}{28}\).
    \(19\frac{11}{28}-18\frac{25}{28}=\frac{39}{28}-\frac{25}{28}=\frac{14}{28}=\frac{1}{2}\).

Ответ: 1) \(44\frac{37}{60}\); 2) \(\frac{2}{9}\); 3) \(\frac{9}{14}\); 4) \(\frac{1}{2}\).