Контрольные задания > 5.169 Найдите значение выражения: a) \(\frac{4}{18}\) + n при n, равном \(\frac{1}{18}\), \(\frac{3}{18}\) и \(\frac{6}{18}\); б) m - \(\frac{1}{9}\) при m, равном \(\frac{6}{9}\), \(\frac{5}{9}\) и \(\frac{2}{9}\); в) \(\frac{4}{15}\) + \(\frac{3}{15}\) + x при x, равном \(\frac{1}{15}\), \(\frac{3}{15}\) и \(\frac{6}{15}\); г) \(\frac{13}{19}\) - \(\frac{3}{19}\) - z при z, равном \(\frac{3}{19}\), \(\frac{5}{19}\) и \(\frac{7}{19}\).
Вопрос:

5.169 Найдите значение выражения: a) \(\frac{4}{18}\) + n при n, равном \(\frac{1}{18}\), \(\frac{3}{18}\) и \(\frac{6}{18}\); б) m - \(\frac{1}{9}\) при m, равном \(\frac{6}{9}\), \(\frac{5}{9}\) и \(\frac{2}{9}\); в) \(\frac{4}{15}\) + \(\frac{3}{15}\) + x при x, равном \(\frac{1}{15}\), \(\frac{3}{15}\) и \(\frac{6}{15}\); г) \(\frac{13}{19}\) - \(\frac{3}{19}\) - z при z, равном \(\frac{3}{19}\), \(\frac{5}{19}\) и \(\frac{7}{19}\).

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Ответ:

a) \(\frac{4}{18}\) + n при n, равном \(\frac{1}{18}\), \(\frac{3}{18}\) и \(\frac{6}{18}\);

  1. Если n = \(\frac{1}{18}\), то \(\frac{4}{18}\) + \(\frac{1}{18}\) = \(\frac{5}{18}\)
  2. Если n = \(\frac{3}{18}\), то \(\frac{4}{18}\) + \(\frac{3}{18}\) = \(\frac{7}{18}\)
  3. Если n = \(\frac{6}{18}\), то \(\frac{4}{18}\) + \(\frac{6}{18}\) = \(\frac{10}{18}\) = \(\frac{5}{9}\)

Ответ: \(\frac{5}{18}\); \(\frac{7}{18}\); \(\frac{5}{9}\)

б) m - \(\frac{1}{9}\) при m, равном \(\frac{6}{9}\), \(\frac{5}{9}\) и \(\frac{2}{9}\);

  1. Если m = \(\frac{6}{9}\), то \(\frac{6}{9}\) - \(\frac{1}{9}\) = \(\frac{5}{9}\)
  2. Если m = \(\frac{5}{9}\), то \(\frac{5}{9}\) - \(\frac{1}{9}\) = \(\frac{4}{9}\)
  3. Если m = \(\frac{2}{9}\), то \(\frac{2}{9}\) - \(\frac{1}{9}\) = \(\frac{1}{9}\)

Ответ: \(\frac{5}{9}\); \(\frac{4}{9}\); \(\frac{1}{9}\)

в) \(\frac{4}{15}\) + \(\frac{3}{15}\) + x при x, равном \(\frac{1}{15}\), \(\frac{3}{15}\) и \(\frac{6}{15}\);

  1. Если x = \(\frac{1}{15}\), то \(\frac{4}{15}\) + \(\frac{3}{15}\) + \(\frac{1}{15}\) = \(\frac{4+3+1}{15}\) = \(\frac{8}{15}\)
  2. Если x = \(\frac{3}{15}\), то \(\frac{4}{15}\) + \(\frac{3}{15}\) + \(\frac{3}{15}\) = \(\frac{4+3+3}{15}\) = \(\frac{10}{15}\) = \(\frac{2}{3}\)
  3. Если x = \(\frac{6}{15}\), то \(\frac{4}{15}\) + \(\frac{3}{15}\) + \(\frac{6}{15}\) = \(\frac{4+3+6}{15}\) = \(\frac{13}{15}\)

Ответ: \(\frac{8}{15}\); \(\frac{2}{3}\); \(\frac{13}{15}\)

г) \(\frac{13}{19}\) - \(\frac{3}{19}\) - z при z, равном \(\frac{3}{19}\), \(\frac{5}{19}\) и \(\frac{7}{19}\).

  1. Если z = \(\frac{3}{19}\), то \(\frac{13}{19}\) - \(\frac{3}{19}\) - \(\frac{3}{19}\) = \(\frac{13-3-3}{19}\) = \(\frac{7}{19}\)
  2. Если z = \(\frac{5}{19}\), то \(\frac{13}{19}\) - \(\frac{3}{19}\) - \(\frac{5}{19}\) = \(\frac{13-3-5}{19}\) = \(\frac{5}{19}\)
  3. Если z = \(\frac{7}{19}\), то \(\frac{13}{19}\) - \(\frac{3}{19}\) - \(\frac{7}{19}\) = \(\frac{13-3-7}{19}\) = \(\frac{3}{19}\)

Ответ: \(\frac{7}{19}\); \(\frac{5}{19}\); \(\frac{3}{19}\)

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