1 Вычислите: а) \(\frac{3}{4} + \frac{4}{5}\); б) \(\frac{2}{3} + \frac{1}{7}\); в) \(\frac{2}{13} + 0\); г) \(\frac{5}{9} + \frac{2}{11}\); д) \(\frac{5}{12} + \frac{3}{4}\); e) \(\frac{5}{6} + \frac{3}{8}\).

Вычислим суммы дробей, приведя их к общему знаменателю.

1. \(\frac{3}{4} + \frac{4}{5} = \frac{3 \cdot 5}{4 \cdot 5} + \frac{4 \cdot 4}{5 \cdot 4} = \frac{15}{20} + \frac{16}{20} = \frac{15 + 16}{20} = \frac{31}{20}\)
2. \(\frac{2}{3} + \frac{1}{7} = \frac{2 \cdot 7}{3 \cdot 7} + \frac{1 \cdot 3}{7 \cdot 3} = \frac{14}{21} + \frac{3}{21} = \frac{14 + 3}{21} = \frac{17}{21}\)
3. \(\frac{2}{13} + 0 = \frac{2}{13}\)
4. \(\frac{5}{9} + \frac{2}{11} = \frac{5 \cdot 11}{9 \cdot 11} + \frac{2 \cdot 9}{11 \cdot 9} = \frac{55}{99} + \frac{18}{99} = \frac{55 + 18}{99} = \frac{73}{99}\)
5. \(\frac{5}{12} + \frac{3}{4} = \frac{5}{12} + \frac{3 \cdot 3}{4 \cdot 3} = \frac{5}{12} + \frac{9}{12} = \frac{5 + 9}{12} = \frac{14}{12} = \frac{7}{6}\)
6. \(\frac{5}{6} + \frac{3}{8} = \frac{5 \cdot 4}{6 \cdot 4} + \frac{3 \cdot 3}{8 \cdot 3} = \frac{20}{24} + \frac{9}{24} = \frac{20 + 9}{24} = \frac{29}{24}\)

Ответ:

1. \(\frac{31}{20}\);
2. \(\frac{17}{21}\);
3. \(\frac{2}{13}\);
4. \(\frac{73}{99}\);
5. \(\frac{7}{6}\);
6. \(\frac{29}{24}\).