5.227 Найдите значение выражения: a) 6/19 + 3/19 + 15/19 б) 19/21 - 17/21 + 9/21 в) 25/32 - 6/32 + 19/32 г) (19/23 - 8/23) + (16/23 - 11/23)

Решение:

а)

\[ \frac{6}{19} + \frac{3}{19} + \frac{15}{19} = \frac{6+3+15}{19} = \frac{24}{19} \]

б)

\[ \frac{19}{21} - \frac{17}{21} + \frac{9}{21} = \frac{19-17+9}{21} = \frac{2+9}{21} = \frac{11}{21} \]

в)

\[ \frac{25}{32} - \frac{6}{32} + \frac{19}{32} = \frac{25-6+19}{32} = \frac{19+19}{32} = \frac{38}{32} = \frac{19}{16} \]

г)

\[ \left( \frac{19}{23} - \frac{8}{23} \right) + \left( \frac{16}{23} - \frac{11}{23} \right) = \left( \frac{19-8}{23} \right) + \left( \frac{16-11}{23} \right) = \frac{11}{23} + \frac{5}{23} = \frac{11+5}{23} = \frac{16}{23} \]

Ответ: а) \(\frac{24}{19}\), б) \(\frac{11}{21}\), в) \(\frac{19}{16}\), г) \(\frac{16}{23}\)