Сравните выражения: а) \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) 7\frac{5}{10} + \frac{3}{14} и 8\frac{3}{8} - \frac{9}{16}

Ответ:

• а) \frac{3}{17} + \frac{6}{17} < \frac{2}{17} + \frac{8}{17}
• б) \frac{7}{19} - \frac{3}{19} = \frac{9}{16} - \frac{5}{16}
• в) 7\frac{5}{10} + \frac{3}{14} > 8\frac{3}{8} - \frac{9}{16}

Ответ:

• а) \(\frac{3}{17} + \frac{6}{17} = \frac{9}{17}\) и \(\frac{2}{17} + \frac{8}{17} = \frac{10}{17}\). Так как \(\frac{9}{17} < \frac{10}{17}\), то \(\frac{3}{17} + \frac{6}{17} < \frac{2}{17} + \frac{8}{17}\)
• б) \(\frac{7}{19} - \frac{3}{19} = \frac{4}{19}\) и \(\frac{9}{16} - \frac{5}{16} = \frac{4}{16} = \frac{1}{4}\). Приведем к общему знаменателю 19 и 4. \(\frac{4}{19} = \frac{16}{76}\) и \(\frac{1}{4} = \frac{19}{76}\). Так как \(\frac{16}{76} < \frac{19}{76}\), то \(\frac{7}{19} - \frac{3}{19} = \frac{9}{16} - \frac{5}{16}\)
• в) \(7\frac{5}{10} + \frac{3}{14} = 7\frac{1}{2} + \frac{3}{14} = 7\frac{7}{14} + \frac{3}{14} = 7\frac{10}{14} = 7\frac{5}{7}\) и \(8\frac{3}{8} - \frac{9}{16} = 8\frac{6}{16} - \frac{9}{16} = 7\frac{22}{16} - \frac{9}{16} = 7\frac{13}{16}\). \(7\frac{5}{7} = 7\frac{80}{112}\) и \(7\frac{13}{16} = 7\frac{91}{112}\). Так как \(7\frac{80}{112} < 7\frac{91}{112}\), то \(7\frac{5}{10} + \frac{3}{14} < 8\frac{3}{8} - \frac{9}{16}\)

Ответ:

• а) \frac{3}{17} + \frac{6}{17} < \frac{2}{17} + \frac{8}{17}
• б) \frac{7}{19} - \frac{3}{19} = \frac{9}{16} - \frac{5}{16}
• в) 7\frac{5}{10} + \frac{3}{14} > 8\frac{3}{8} - \frac{9}{16}