5.409 Найдите сумму или разность: а) \(\frac{1}{5} + \frac{1}{7}\); б) \(\frac{1}{4} + \frac{1}{9}\); в) \(\frac{4}{7} + \frac{4}{9}\); г) \(\frac{1}{2} + \frac{5}{7}\); д) \(\frac{9}{11} + 0\); е) \(\frac{3}{4} - \frac{3}{5}\); ж) \(\frac{1}{3} - \frac{1}{4}\); з) \(\frac{3}{7} - \frac{2}{9}\); и) \(\frac{4}{9} - \frac{2}{5}\); к) \(\frac{11}{13} - 0\); л) \(\frac{2}{3} + \frac{3}{5}\); м) \(\frac{2}{3} + \frac{3}{12}\).

Решим примеры на сложение и вычитание дробей.

1. а) \(\frac{1}{5} + \frac{1}{7} = \frac{1 \cdot 7 + 1 \cdot 5}{35} = \frac{7 + 5}{35} = \frac{12}{35}\)
2. б) \(\frac{1}{4} + \frac{1}{9} = \frac{1 \cdot 9 + 1 \cdot 4}{36} = \frac{9 + 4}{36} = \frac{13}{36}\)
3. в) \(\frac{4}{7} + \frac{4}{9} = \frac{4 \cdot 9 + 4 \cdot 7}{63} = \frac{36 + 28}{63} = \frac{64}{63}\)
4. г) \(\frac{1}{2} + \frac{5}{7} = \frac{1 \cdot 7 + 5 \cdot 2}{14} = \frac{7 + 10}{14} = \frac{17}{14}\)
5. д) \(\frac{9}{11} + 0 = \frac{9}{11}\)
6. е) \(\frac{3}{4} - \frac{3}{5} = \frac{3 \cdot 5 - 3 \cdot 4}{20} = \frac{15 - 12}{20} = \frac{3}{20}\)
7. ж) \(\frac{1}{3} - \frac{1}{4} = \frac{1 \cdot 4 - 1 \cdot 3}{12} = \frac{4 - 3}{12} = \frac{1}{12}\)
8. з) \(\frac{3}{7} - \frac{2}{9} = \frac{3 \cdot 9 - 2 \cdot 7}{63} = \frac{27 - 14}{63} = \frac{13}{63}\)
9. и) \(\frac{4}{9} - \frac{2}{5} = \frac{4 \cdot 5 - 2 \cdot 9}{45} = \frac{20 - 18}{45} = \frac{2}{45}\)
10. к) \(\frac{11}{13} - 0 = \frac{11}{13}\)
11. л) \(\frac{2}{3} + \frac{3}{5} = \frac{2 \cdot 5 + 3 \cdot 3}{15} = \frac{10 + 9}{15} = \frac{19}{15}\)
12. м) \(\frac{2}{3} + \frac{3}{12} = \frac{2 \cdot 4 + 3}{12} = \frac{8 + 3}{12} = \frac{11}{12}\)

Ответ:

а) \(\frac{12}{35}\); б) \(\frac{13}{36}\); в) \(\frac{64}{63}\); г) \(\frac{17}{14}\); д) \(\frac{9}{11}\); е) \(\frac{3}{20}\); ж) \(\frac{1}{12}\); з) \(\frac{13}{63}\); и) \(\frac{2}{45}\); к) \(\frac{11}{13}\); л) \(\frac{19}{15}\); м) \(\frac{11}{12}\)