270. Вычислите: 1) \(\frac{1}{4} + \frac{3}{5}\); 2) \(\frac{9}{11} - \frac{2}{5}\); 3) \(\frac{13}{16} - \frac{9}{32}\); 4) \(\frac{3}{28} + \frac{5}{14}\); 5) \(\frac{14}{15} - \frac{7}{10}\); 6) \(\frac{3}{8} + \frac{1}{6}\);

Решение:

1. \(\frac{1}{4} + \frac{3}{5} = \frac{1 \cdot 5}{4 \cdot 5} + \frac{3 \cdot 4}{5 \cdot 4} = \frac{5}{20} + \frac{12}{20} = \frac{5 + 12}{20} = \frac{17}{20}\)
2. \(\frac{9}{11} - \frac{2}{5} = \frac{9 \cdot 5}{11 \cdot 5} - \frac{2 \cdot 11}{5 \cdot 11} = \frac{45}{55} - \frac{22}{55} = \frac{45 - 22}{55} = \frac{23}{55}\)
3. \(\frac{13}{16} - \frac{9}{32} = \frac{13 \cdot 2}{16 \cdot 2} - \frac{9}{32} = \frac{26}{32} - \frac{9}{32} = \frac{26 - 9}{32} = \frac{17}{32}\)
4. \(\frac{3}{28} + \frac{5}{14} = \frac{3}{28} + \frac{5 \cdot 2}{14 \cdot 2} = \frac{3}{28} + \frac{10}{28} = \frac{3 + 10}{28} = \frac{13}{28}\)
5. \(\frac{14}{15} - \frac{7}{10} = \frac{14 \cdot 2}{15 \cdot 2} - \frac{7 \cdot 3}{10 \cdot 3} = \frac{28}{30} - \frac{21}{30} = \frac{28 - 21}{30} = \frac{7}{30}\)
6. \(\frac{3}{8} + \frac{1}{6} = \frac{3 \cdot 3}{8 \cdot 3} + \frac{1 \cdot 4}{6 \cdot 4} = \frac{9}{24} + \frac{4}{24} = \frac{9 + 4}{24} = \frac{13}{24}\)

Ответ: 1) \(\frac{17}{20}\); 2) \(\frac{23}{55}\); 3) \(\frac{17}{32}\); 4) \(\frac{13}{28}\); 5) \(\frac{7}{30}\); 6) \(\frac{13}{24}\)