Вопрос:

98. Найди значение выражения:

Ответ:

98. Найди значение выражения:

  1. \( \frac{1}{2} + \frac{2}{3} + \frac{3}{4} = \frac{6}{12} + \frac{8}{12} + \frac{9}{12} = \frac{23}{12} = 1\frac{11}{12} \)
  2. \( \frac{7}{8} + \frac{1}{6} - \frac{2}{3} = \frac{21}{24} + \frac{4}{24} - \frac{16}{24} = \frac{25 - 16}{24} = \frac{9}{24} = \frac{3}{8} \)
  3. \( \frac{9}{10} - \frac{3}{5} + \frac{5}{7} = \frac{63}{70} - \frac{42}{70} + \frac{50}{70} = \frac{21 + 50}{70} = \frac{71}{70} = 1\frac{1}{70} \)
  4. \( \frac{5}{24} - \frac{1}{60} - \frac{1}{40} = \frac{25}{120} - \frac{2}{120} - \frac{3}{120} = \frac{25 - 5}{120} = \frac{20}{120} = \frac{1}{6} \)
  5. \( \frac{5}{14} + \frac{10}{21} - \frac{3}{4} = \frac{15}{42} + \frac{20}{42} - \frac{3}{4} = \frac{35}{42} - \frac{3}{4} = \frac{5}{6} - \frac{3}{4} = \frac{10}{12} - \frac{9}{12} = \frac{1}{12} \)
  6. \( \frac{5}{6} - \frac{3}{16} + \frac{5}{12} = \frac{40}{48} - \frac{9}{48} + \frac{20}{48} = \frac{31 + 20}{48} = \frac{51}{48} = 1\frac{3}{48} = 1\frac{1}{16} \)
  7. \( \left( \frac{7}{10} + \frac{3}{5} \right) - \left( \frac{1}{6} + \frac{2}{3} \right) = \left( \frac{7}{10} + \frac{6}{10} \right) - \left( \frac{1}{6} + \frac{4}{6} \right) = \frac{13}{10} - \frac{5}{6} = \frac{39}{30} - \frac{25}{30} = \frac{14}{30} = \frac{7}{15} \)
  8. \( \frac{2}{3} - \left( \frac{1}{20} + \frac{2}{9} \right) - \frac{5}{18} = \frac{2}{3} - \left( \frac{9}{180} + \frac{40}{180} \right) - \frac{5}{18} = \frac{2}{3} - \frac{49}{180} - \frac{5}{18} = \frac{120}{180} - \frac{49}{180} - \frac{50}{180} = \frac{120 - 99}{180} = \frac{21}{180} = \frac{7}{60} \)
  9. \( \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7} = \frac{140}{420} + \frac{105}{420} + \frac{84}{420} + \frac{70}{420} + \frac{60}{420} = \frac{140 + 105 + 84 + 70 + 60}{420} = \frac{459}{420} = \frac{153}{140} = 1\frac{13}{140} \)
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