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) $$\frac{7}{10} \cdot \frac{5}{14}$$ и $$\frac{3}{8} : \frac{16}{9}$$.

Сравним выражения:

1. а) $$\frac{3}{17} + \frac{6}{17}$$ и $$\frac{2}{17} + \frac{8}{17}$$

   $$\frac{3}{17} + \frac{6}{17} = \frac{3+6}{17} = \frac{9}{17}$$

   $$\frac{2}{17} + \frac{8}{17} = \frac{2+8}{17} = \frac{10}{17}$$

   Так как $$\frac{9}{17} < \frac{10}{17}$$, то $$\frac{3}{17} + \frac{6}{17} < \frac{2}{17} + \frac{8}{17}$$

2. б) $$\frac{7}{19} - \frac{3}{19}$$ и $$\frac{9}{16} - \frac{5}{16}$$

   $$\frac{7}{19} - \frac{3}{19} = \frac{7-3}{19} = \frac{4}{19}$$

   $$\frac{9}{16} - \frac{5}{16} = \frac{9-5}{16} = \frac{4}{16} = \frac{1}{4}$$

   Приведем дроби к общему знаменателю (76):

   $$\frac{4}{19} = \frac{4 \cdot 4}{19 \cdot 4} = \frac{16}{76}$$

   $$\frac{1}{4} = \frac{1 \cdot 19}{4 \cdot 19} = \frac{19}{76}$$

   Так как $$\frac{16}{76} < \frac{19}{76}$$, то $$\frac{7}{19} - \frac{3}{19} < \frac{9}{16} - \frac{5}{16}$$

3. в) $$\frac{7}{10} \cdot \frac{5}{14}$$ и $$\frac{3}{8} : \frac{16}{9}$$

   $$\frac{7}{10} \cdot \frac{5}{14} = \frac{7 \cdot 5}{10 \cdot 14} = \frac{35}{140} = \frac{1}{4}$$

   $$\frac{3}{8} : \frac{16}{9} = \frac{3}{8} \cdot \frac{9}{16} = \frac{3 \cdot 9}{8 \cdot 16} = \frac{27}{128}$$

   Приведем дроби к общему знаменателю (512):

   $$\frac{1}{4} = \frac{1 \cdot 128}{4 \cdot 128} = \frac{128}{512}$$

   $$\frac{27}{128} = \frac{27 \cdot 4}{128 \cdot 4} = \frac{108}{512}$$

   Так как $$\frac{128}{512} > \frac{108}{512}$$, то $$\frac{7}{10} \cdot \frac{5}{14} > \frac{3}{8} : \frac{16}{9}$$

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) $$\frac{7}{10} \cdot \frac{5}{14} > \frac{3}{8} : \frac{16}{9}$$