Вопрос:

3. Выполните действия: а) (9 - 2 3/11) + (2 + 9/11); б) 28 2/21 - (14 17/21 + 8/21).

Ответ:

3. Выполните действия:

  1. а) \( \left(9 - 2 \frac{3}{11}\right) + \left(2 + \frac{9}{11}\right) = \left(9 - (2 + \frac{3}{11})\right) + \left(2 + \frac{9}{11}\right) = 9 - 2 - \frac{3}{11} + 2 + \frac{9}{11} = (9 - 2 + 2) + (\frac{9}{11} - \frac{3}{11}) = 9 + \frac{6}{11} = 9 \frac{6}{11} \)
  2. б) \( 28 \frac{2}{21} - \left(14 \frac{17}{21} + \frac{8}{21}\right) = 28 \frac{2}{21} - \left(14 + \frac{17+8}{21}\right) = 28 \frac{2}{21} - \left(14 + \frac{25}{21}\right) = 28 \frac{2}{21} - \left(14 + 1 \frac{4}{21}\right) = 28 \frac{2}{21} - 15 \frac{4}{21} \).
  3. \( 28 \frac{2}{21} - 15 \frac{4}{21} = (27 + \frac{21+2}{21}) - 15 \frac{4}{21} = 27 \frac{23}{21} - 15 \frac{4}{21} = (27 - 15) + (\frac{23}{21} - \frac{4}{21}) = 12 + \frac{19}{21} = 12 \frac{19}{21} \)

Ответ: а) \( 9 \frac{6}{11} \); б) \( 12 \frac{19}{21} \).

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