Вопрос:

2. Найдите значение выражения:

Ответ:

2. Найдите значение выражения:

  1. \( \frac{1}{2} + \frac{2}{3} + \frac{3}{4} = \frac{6+8+9}{12} = \frac{23}{12} = 1\frac{11}{12} \)
  2. \( \frac{7}{8} + \frac{1}{6} - \frac{2}{3} = \frac{21+4-16}{24} = \frac{9}{24} = \frac{3}{8} \)
  3. \( \frac{9}{10} + \frac{3}{5} + \frac{7}{7} = \frac{9}{10} + \frac{6}{10} + 1 = \frac{15}{10} + 1 = 1\frac{5}{10} + 1 = 1\frac{1}{2} + 1 = 2\frac{1}{2} \)
  4. \( \frac{5}{24} - \frac{1}{60} - \frac{1}{40} = \frac{25-2-3}{120} = \frac{20}{120} = \frac{1}{6} \)
  5. \( \frac{7}{14} + \frac{21}{21} - \frac{4}{4} = \frac{1}{2} + 1 - 1 = \frac{1}{2} \)
  6. \( \frac{5}{6} - \frac{3}{16} + \frac{5}{12} = \frac{10+5-6}{24} = \frac{9}{24} = \frac{3}{8} \)
  7. \( (\frac{7}{10} + \frac{3}{5}) - (\frac{1}{6} + \frac{2}{3}) = (\frac{7+6}{10}) - (\frac{1+4}{6}) = \frac{13}{10} - \frac{5}{6} = \frac{39-25}{30} = \frac{14}{30} = \frac{7}{15} \)
  8. \( \frac{2}{3} - (\frac{1}{20} + \frac{2}{9}) - \frac{5}{18} = \frac{2}{3} - (\frac{9+40}{180}) - \frac{5}{18} = \frac{2}{3} - \frac{49}{180} - \frac{5}{18} = \frac{120-49-50}{180} = \frac{21}{180} = \frac{7}{60} \)
  9. \( \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7} = \frac{140+105+84+70+60}{420} = \frac{459}{420} = \frac{153}{140} = 1\frac{13}{140} \)

Ответ: 1) \(1\frac{11}{12}\); 2) \(\frac{3}{8}\); 3) \(2\frac{1}{2}\); 4) \(\frac{1}{6}\); 5) \(\frac{1}{2}\); 6) \(\frac{3}{8}\); 7) \(\frac{7}{15}\); 8) \(\frac{7}{60}\); 9) \(1\frac{13}{140}\).