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:

1. a) \[\frac{3}{17}+\frac{6}{17} = \frac{9}{17}\] \[\frac{2}{17}+\frac{8}{17}=\frac{10}{17}\] \[\frac{9}{17} < \frac{10}{17}\]
2. б) \[\frac{7}{19}-\frac{3}{19} = \frac{4}{19}\] \[\frac{9}{16}-\frac{5}{16}=\frac{4}{16} = \frac{1}{4}\] Чтобы сравнить \(\frac{4}{19}\) и \(\frac{1}{4}\), приведем их к общему знаменателю: \[\frac{4}{19} = \frac{4 \times 4}{19 \times 4} = \frac{16}{76}\] \[\frac{1}{4} = \frac{1 \times 19}{4 \times 19} = \frac{19}{76}\] \[\frac{16}{76} < \frac{19}{76}\]
3. в) \[\frac{7}{10}-\frac{5}{14} = \frac{7 \times 14 - 5 \times 10}{10 \times 14} = \frac{98-50}{140}=\frac{48}{140}=\frac{12}{35}\] \[\frac{3}{8}+\frac{9}{16}=\frac{6+9}{16}=\frac{15}{16}\]Чтобы сравнить \(\frac{12}{35}\) и \(\frac{15}{16}\), приведем их к общему знаменателю: \[\frac{12}{35} = \frac{12 \times 16}{35 \times 16} = \frac{192}{560}\] \[\frac{15}{16} = \frac{15 \times 35}{16 \times 35} = \frac{525}{560}\] \[\frac{192}{560} < \frac{525}{560}\]

Ответ: