1. Выполните сложение: a) \(\frac{3}{4} + \frac{2}{3}\) б) \(\frac{3}{10} + \frac{2}{15}\) в) \(\frac{4}{9} + \frac{1}{6}\) г) \(\frac{7}{15} + \frac{3}{40}\) д) \(\frac{6}{7} + \frac{9}{21}\) e) \(\frac{11}{20} + \frac{6}{15}\)

Решение:

1. а) \(\frac{3}{4} + \frac{2}{3} = \frac{3 \times 3}{4 \times 3} + \frac{2 \times 4}{3 \times 4} = \frac{9}{12} + \frac{8}{12} = \frac{9+8}{12} = \frac{17}{12}\)
2. б) \(\frac{3}{10} + \frac{2}{15} = \frac{3 \times 3}{10 \times 3} + \frac{2 \times 2}{15 \times 2} = \frac{9}{30} + \frac{4}{30} = \frac{9+4}{30} = \frac{13}{30}\)
3. в) \(\frac{4}{9} + \frac{1}{6} = \frac{4 \times 2}{9 \times 2} + \frac{1 \times 3}{6 \times 3} = \frac{8}{18} + \frac{3}{18} = \frac{8+3}{18} = \frac{11}{18}\)
4. г) \(\frac{7}{15} + \frac{3}{40} = \frac{7 \times 8}{15 \times 8} + \frac{3 \times 3}{40 \times 3} = \frac{56}{120} + \frac{9}{120} = \frac{56+9}{120} = \frac{65}{120} = \frac{13}{24}\)
5. д) \(\frac{6}{7} + \frac{9}{21} = \frac{6 \times 3}{7 \times 3} + \frac{9}{21} = \frac{18}{21} + \frac{9}{21} = \frac{18+9}{21} = \frac{27}{21} = \frac{9}{7}\)
6. е) \(\frac{11}{20} + \frac{6}{15} = \frac{11 \times 3}{20 \times 3} + \frac{6 \times 4}{15 \times 4} = \frac{33}{60} + \frac{24}{60} = \frac{33+24}{60} = \frac{57}{60} = \frac{19}{20}\)

Ответ: а) \(\frac{17}{12}\), б) \(\frac{13}{30}\), в) \(\frac{11}{18}\), г) \(\frac{13}{24}\), д) \(\frac{9}{7}\), е) \(\frac{19}{20}\)