2.192 Сравните дроби: a) \(\frac{2}{3}\) и \(\frac{8}{21}\); в) \(\frac{3}{8}\) и \(\frac{17}{40}\); д) \(\frac{1}{6}\) и \(\frac{4}{21}\); б) \(\frac{4}{15}\) и \(\frac{2}{5}\); г) \(\frac{5}{6}\) и \(\frac{31}{36}\); e) \(\frac{13}{18}\) и \(\frac{11}{15}\); ж) \(\frac{17}{125}\) и \(\frac{23}{165}\); з) \(\frac{19}{77}\) и \(\frac{43}{176}\);

a) \(\frac{2}{3} = \frac{2 \cdot 7}{3 \cdot 7} = \frac{14}{21}\). Так как \(\frac{14}{21} > \frac{8}{21}\), то \(\frac{2}{3} > \frac{8}{21}\). в) \(\frac{3}{8} = \frac{3 \cdot 5}{8 \cdot 5} = \frac{15}{40}\). Так как \(\frac{15}{40} < \frac{17}{40}\), то \(\frac{3}{8} < \(\frac{17}{40}\). д) \(\frac{1}{6} = \frac{1 \cdot 7}{6 \cdot 7} = \frac{7}{42}\), \(\frac{4}{21} = \frac{4 \cdot 2}{21 \cdot 2} = \frac{8}{42}\). Так как \(\frac{7}{42} < \frac{8}{42}\), то \(\frac{1}{6} < \frac{4}{21}\). б) \(\frac{4}{15}\) и \(\frac{2}{5} = \frac{2 \cdot 3}{5 \cdot 3} = \frac{6}{15}\). Так как \(\frac{4}{15} < \frac{6}{15}\), то \(\frac{4}{15} < \frac{2}{5}\). г) \(\frac{5}{6} = \frac{5 \cdot 6}{6 \cdot 6} = \frac{30}{36}\). Так как \(\frac{30}{36} < \frac{31}{36}\), то \(\frac{5}{6} < \frac{31}{36}\). e) \(\frac{13}{18} = \frac{13 \cdot 5}{18 \cdot 5} = \frac{65}{90}\), \(\frac{11}{15} = \frac{11 \cdot 6}{15 \cdot 6} = \frac{66}{90}\). Так как \(\frac{65}{90} < \frac{66}{90}\), то \(\frac{13}{18} < \frac{11}{15}\). ж) \(\frac{17}{125} = \frac{17 \cdot 33}{125 \cdot 33} = \frac{561}{4125}\), \(\frac{23}{165} = \frac{23 \cdot 25}{165 \cdot 25} = \frac{575}{4125}\). Так как \(\frac{561}{4125} < \frac{575}{4125}\), то \(\frac{17}{125} < \frac{23}{165}\). з) \(\frac{19}{77} = \frac{19 \cdot 16}{77 \cdot 16} = \frac{304}{1232}\), \(\frac{43}{176} = \frac{43 \cdot 7}{176 \cdot 7} = \frac{301}{1232}\). Так как \(\frac{304}{1232} > \frac{301}{1232}\), то \(\frac{19}{77} > \frac{43}{176}\). Ответ: a) \(\frac{2}{3} > \frac{8}{21}\); в) \(\frac{3}{8} < \frac{17}{40}\); д) \(\frac{1}{6} < \frac{4}{21}\); б) \(\frac{4}{15} < \frac{2}{5}\); г) \(\frac{5}{6} < \frac{31}{36}\); e) \(\frac{13}{18} < \frac{11}{15}\); ж) \(\frac{17}{125} < \frac{23}{165}\); з) \(\frac{19}{77} > \frac{43}{176}\).