6.241 Сравните выражения: a) \(\frac{3}{17}\) + \(\frac{6}{17}\) и \(\frac{2}{17}\) + \(\frac{8}{17}\) б) \(\frac{7}{19}\) - \(\frac{3}{19}\) и \(\frac{9}{16}\) - \(\frac{5}{16}\) в) \(\frac{7}{10}\) + \(\frac{5}{14}\) и \(\frac{3}{8}\) + \(\frac{9}{16}\)

Ответ: a) \(\frac{9}{17} < \frac{10}{17}\); б) \(\frac{4}{19} < \(\frac{4}{16}\); в) \(\frac{74}{70} > \(\frac{15}{16}\)

1. а) \(\frac{3}{17}\) + \(\frac{6}{17}\) = \(\frac{9}{17}\); \(\frac{2}{17}\) + \(\frac{8}{17}\) = \(\frac{10}{17}\). Сравниваем: \(\frac{9}{17} < \frac{10}{17}\)
2. б) \(\frac{7}{19}\) - \(\frac{3}{19}\) = \(\frac{4}{19}\); \(\frac{9}{16}\) - \(\frac{5}{16}\) = \(\frac{4}{16}\). Сравниваем: \(\frac{4}{19} < \(\frac{4}{16}\)
3. в) \(\frac{7}{10}\) + \(\frac{5}{14}\) = \(\frac{7 \cdot 7}{10 \cdot 7}\) + \(\frac{5 \cdot 5}{14 \cdot 5}\) = \(\frac{49}{70}\) + \(\frac{25}{70}\) = \(\frac{74}{70}\); \(\frac{3}{8}\) + \(\frac{9}{16}\) = \(\frac{3 \cdot 2}{8 \cdot 2}\) + \(\frac{9}{16}\) = \(\frac{6}{16}\) + \(\frac{9}{16}\) = \(\frac{15}{16}\). Сравниваем: \(\frac{74}{70} > \(\frac{15}{16}\)

Ответ: a) \(\frac{9}{17} < \frac{10}{17}\); б) \(\frac{4}{19} < \(\frac{4}{16}\); в) \(\frac{74}{70} > \(\frac{15}{16}\)