3. Сравните обыкновенные дроби: 4/12 и 1/5 11/14 и 14/21 7/15 и 4/10 5/18 и 9/12

Ответ: 1) 4/12 > 1/5; 2) 11/14 > 14/21; 3) 7/15 < 4/10; 4) 5/18 < 9/12

Решение:

1. Сравним \(\frac{4}{12}\) и \(\frac{1}{5}\): \[\frac{4}{12} = \frac{1}{3} = \frac{5}{15}\] \[\frac{1}{5} = \frac{3}{15}\] \[\frac{5}{15} > \frac{3}{15}\), значит \(\frac{4}{12} > \frac{1}{5}\]
2. Сравним \(\frac{11}{14}\) и \(\frac{14}{21}\): \[\frac{14}{21} = \frac{2}{3}\] \[\frac{11}{14} = \frac{33}{42}\] \[\frac{2}{3} = \frac{28}{42}\] \[\frac{33}{42} > \frac{28}{42}\), значит \(\frac{11}{14} > \frac{14}{21}\]
3. Сравним \(\frac{7}{15}\) и \(\frac{4}{10}\): \[\frac{7}{15} = \frac{14}{30}\] \[\frac{4}{10} = \frac{2}{5} = \frac{12}{30}\] \[\frac{14}{30} > \frac{12}{30}\), значит \(\frac{7}{15} > \frac{4}{10}\]
4. Сравним \(\frac{5}{18}\) и \(\frac{9}{12}\): \[\frac{5}{18} = \frac{10}{36}\] \[\frac{9}{12} = \frac{3}{4} = \frac{27}{36}\] \[\frac{10}{36} < \frac{27}{36}\), значит \(\frac{5}{18} < \frac{9}{12}\]

Ответ: 1) 4/12 > 1/5; 2) 11/14 > 14/21; 3) 7/15 < 4/10; 4) 5/18 < 9/12