5.445 Вычислите: a) \(\frac{1}{2} + \frac{1}{3}\); г) \(\frac{3}{7} + \(\frac{4}{9}\); ж) \(\frac{1}{6} + \(\frac{1}{3}\); к) \(\frac{7}{15} - \(\frac{3}{10}\); б) \(\frac{1}{3} + \(\frac{2}{7}\); д) \(\frac{5}{9} - \(\frac{1}{6}\); з) \(\frac{9}{5} - \(\frac{7}{10}\); л) \(\frac{3}{8} + \(\frac{5}{12}\); в) \(\frac{2}{5} + \(\frac{1}{3}\); е) \(\frac{3}{4} - \(\frac{1}{3}\); и) \(\frac{1}{2} - \(\frac{3}{8}\); м) \(\frac{5}{9} - \(\frac{1}{6}\); н) \(\frac{5}{11} + \(\frac{5}{11}\); о) \(\frac{17}{30} - \(\frac{17}{35}\); п) \(\frac{17}{35} - \(\frac{17}{35}\);

Ответ: a) \(\frac{5}{6}\); б) \(\frac{13}{21}\); в) \(\frac{11}{15}\); г) \(\frac{55}{63}\); д) \(\frac{7}{18}\); e) \(\frac{5}{12}\); ж) \(\frac{1}{2}\); з) \(\frac{11}{10}\); и) \(\frac{1}{8}\); к) \(\frac{5}{30}\); л) \(\frac{19}{24}\); м) \(\frac{7}{18}\); н) \(\frac{10}{11}\); о) \(\frac{17}{210}\); п) 0.

Решение:

1. а) \(\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}\)
2. б) \(\frac{1}{3} + \frac{2}{7} = \frac{7}{21} + \frac{6}{21} = \frac{13}{21}\)
3. в) \(\frac{2}{5} + \frac{1}{3} = \frac{6}{15} + \frac{5}{15} = \frac{11}{15}\)
4. г) \(\frac{3}{7} + \frac{4}{9} = \frac{27}{63} + \frac{28}{63} = \frac{55}{63}\)
5. д) \(\frac{5}{9} - \frac{1}{6} = \frac{10}{18} - \frac{3}{18} = \frac{7}{18}\)
6. е) \(\frac{3}{4} - \frac{1}{3} = \frac{9}{12} - \frac{4}{12} = \frac{5}{12}\)
7. ж) \(\frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2}\)
8. з) \(\frac{9}{5} - \frac{7}{10} = \frac{18}{10} - \frac{7}{10} = \frac{11}{10}\)
9. и) \(\frac{1}{2} - \frac{3}{8} = \frac{4}{8} - \frac{3}{8} = \frac{1}{8}\)
10. к) \(\frac{7}{15} - \frac{3}{10} = \frac{14}{30} - \frac{9}{30} = \frac{5}{30}\)
11. л) \(\frac{3}{8} + \frac{5}{12} = \frac{9}{24} + \frac{10}{24} = \frac{19}{24}\)
12. м) \(\frac{5}{9} - \frac{1}{6} = \frac{10}{18} - \frac{3}{18} = \frac{7}{18}\)
13. н) \(\frac{5}{11} + \frac{5}{11} = \frac{10}{11}\)
14. о) \(\frac{17}{30} - \frac{17}{35} = \frac{17 \cdot 7}{30 \cdot 7} - \frac{17 \cdot 6}{35 \cdot 6} = \frac{119}{210} - \frac{102}{210} = \frac{17}{210}\)
15. п) \(\frac{17}{35} - \frac{17}{35} = 0\)

Ответ: a) \(\frac{5}{6}\); б) \(\frac{13}{21}\); в) \(\frac{11}{15}\); г) \(\frac{55}{63}\); д) \(\frac{7}{18}\); e) \(\frac{5}{12}\); ж) \(\frac{1}{2}\); з) \(\frac{11}{10}\); и) \(\frac{1}{8}\); к) \(\frac{5}{30}\); л) \(\frac{19}{24}\); м) \(\frac{7}{18}\); н) \(\frac{10}{11}\); о) \(\frac{17}{210}\); п) 0.