Вопрос:

Выполните действия: a) 1 2/3 + 3 1/3 - 2 1/3; б) 2 1/6 + 3 2/3 + 4 5/6; в) 7 5/12 - 1 5/6 + 3 1/24; г) 9 7/18 - 6 2/36 + 11 2/9

Ответ:

Решение:

  1. а) 1 2/3 + 3 1/3 - 2 1/3
    \( \frac{5}{3} + \frac{10}{3} - \frac{7}{3} = \frac{5+10-7}{3} = \frac{8}{3} = 2\frac{2}{3} \)
  2. б) 2 1/6 + 3 2/3 + 4 5/6
    \( \frac{13}{6} + \frac{11}{3} + \frac{29}{6} = \frac{13}{6} + \frac{22}{6} + \frac{29}{6} = \frac{13+22+29}{6} = \frac{64}{6} = \frac{32}{3} = 10\frac{2}{3} \)
  3. в) 7 5/12 - 1 5/6 + 3 1/24
    \( 7\frac{5}{12} - 1\frac{5}{6} + 3\frac{1}{24} = \frac{89}{12} - \frac{11}{6} + \frac{73}{24} = \frac{178}{24} - \frac{44}{24} + \frac{73}{24} = \frac{178-44+73}{24} = \frac{207}{24} = \frac{69}{8} = 8\frac{5}{8} \)
  4. г) 9 7/18 - 6 2/36 + 11 2/9
    \( 9\frac{7}{18} - 6\frac{2}{36} + 11\frac{2}{9} = \frac{169}{18} - \frac{218}{36} + \frac{101}{9} = \frac{338}{36} - \frac{218}{36} + \frac{404}{36} = \frac{338-218+404}{36} = \frac{524}{36} = \frac{131}{9} = 14\frac{5}{9} \)

Ответ: а) 2 2/3; б) 10 2/3; в) 8 5/8; г) 14 5/9.