89. Найдите значение выражения:

Решение:

1. \( 6\frac{3}{4} - 2\frac{1}{8} = \frac{27}{4} - \frac{17}{8} = \frac{54}{8} - \frac{17}{8} = \frac{37}{8} = 4\frac{5}{8} \)
2. \( 9\frac{8}{15} - 4\frac{1}{6} + 3\frac{7}{20} = \frac{143}{15} - \frac{25}{6} + \frac{67}{20} = \frac{572}{60} - \frac{250}{60} + \frac{201}{60} = \frac{523}{60} = 8\frac{43}{60} \)
3. \( 7\frac{5}{3} + 3\frac{2}{3} - 8\frac{3}{16} = \frac{26}{3} + \frac{11}{3} - \frac{131}{16} = \frac{37}{3} - \frac{131}{16} = \frac{592 - 393}{48} = \frac{199}{48} = 4\frac{7}{48} \)
4. \( \frac{9}{25} - 4\frac{1}{10} - 2\frac{1}{5} = \frac{9}{25} - \frac{41}{10} - \frac{11}{5} = \frac{18 - 410 - 220}{50} = \frac{-612}{50} = -12\frac{12}{50} = -12\frac{6}{25} \)
5. \( 20 - (3\frac{1}{6} + 2\frac{2}{3}) = 20 - (\frac{19}{6} + \frac{8}{3}) = 20 - (\frac{19}{6} + \frac{16}{6}) = 20 - \frac{35}{6} = \frac{120 - 35}{6} = \frac{85}{6} = 14\frac{1}{6} \)
6. \( 1\frac{5}{6} + (3-1\frac{7}{10}) = \frac{11}{6} + (3 - \frac{17}{10}) = \frac{11}{6} + (\frac{30-17}{10}) = \frac{11}{6} + \frac{13}{10} = \frac{55 + 39}{30} = \frac{94}{30} = \frac{47}{15} = 3\frac{2}{15} \)

Ответ: а) \( 4\frac{5}{8} \); б) \( 8\frac{43}{60} \); в) \( 4\frac{7}{48} \); г) \( -12\frac{6}{25} \); д) \( 14\frac{1}{6} \); е) \( 3\frac{2}{15} \).