47. Вычислите: 1) \(\frac{3}{4} + \frac{5}{7}\) 2) \(\frac{9}{14} - \frac{3}{4}\) 3) \(\frac{11}{12} - \frac{2}{3}\) 4) \(\frac{7}{25} + \frac{4}{10}\) 5) \(\frac{11}{18} - \frac{5}{12}\) 6) \(\frac{13}{18} + \frac{7}{15}\)

Решение:

1. \(\frac{3}{4} + \frac{5}{7} = \frac{3 \cdot 7}{4 \cdot 7} + \frac{5 \cdot 4}{7 \cdot 4} = \frac{21}{28} + \frac{20}{28} = \frac{41}{28}\)
2. \(\frac{9}{14} - \frac{3}{4} = \frac{9 \cdot 2}{14 \cdot 2} - \frac{3 \cdot 7}{4 \cdot 7} = \frac{18}{28} - \frac{21}{28} = -\frac{3}{28}\)
3. \(\frac{11}{12} - \frac{2}{3} = \frac{11}{12} - \frac{2 \cdot 4}{3 \cdot 4} = \frac{11}{12} - \frac{8}{12} = \frac{3}{12} = \frac{1}{4}\)
4. \(\frac{7}{25} + \frac{4}{10} = \frac{7 \cdot 2}{25 \cdot 2} + \frac{4 \cdot 5}{10 \cdot 5} = \frac{14}{50} + \frac{20}{50} = \frac{34}{50} = \frac{17}{25}\)
5. \(\frac{11}{18} - \frac{5}{12} = \frac{11 \cdot 2}{18 \cdot 2} - \frac{5 \cdot 3}{12 \cdot 3} = \frac{22}{36} - \frac{15}{36} = \frac{7}{36}\)
6. \(\frac{13}{18} + \frac{7}{15} = \frac{13 \cdot 5}{18 \cdot 5} + \frac{7 \cdot 6}{15 \cdot 6} = \frac{65}{90} + \frac{42}{90} = \frac{107}{90}\)

Ответ: 1) \(\frac{41}{28}\); 2) -\(\frac{3}{28}\); 3) \(\frac{1}{4}\); 4) \(\frac{17}{25}\); 5) \(\frac{7}{36}\); 6) \(\frac{107}{90}\).