2. Выполнить действия с обыкновенными дробями:

Решение:

1. \( \frac{1}{5} + \frac{1}{3} = \frac{3}{15} + \frac{5}{15} = \frac{8}{15} \)


2. \( \frac{1}{3} : \frac{1}{8} = \frac{1}{3} \cdot 8 = \frac{8}{3} \)


3. \( \frac{1}{4} + \frac{2}{3} = \frac{3}{12} + \frac{8}{12} = \frac{11}{12} \)


4. \( 3 \frac{1}{2} : 1 \frac{1}{4} = \frac{7}{2} : \frac{5}{4} = \frac{7}{2} \cdot \frac{4}{5} = \frac{28}{10} = \frac{14}{5} \)


5. \( \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \)


6. \( 2 \frac{1}{8} \)


7. \( -1 \frac{1}{4} - 3 \frac{1}{3} = -\frac{5}{4} - \frac{10}{3} = -\frac{15}{12} - \frac{40}{12} = -\frac{55}{12} \)


8. \( \frac{3}{15} : \frac{4}{8} = \frac{1}{5} : \frac{1}{2} = \frac{1}{5} \cdot 2 = \frac{2}{5} \)


9. \( 3 \frac{3}{5} - 1 \frac{1}{2} = \frac{18}{5} - \frac{3}{2} = \frac{36}{10} - \frac{15}{10} = \frac{21}{10} \)


10. \( -3 \frac{1}{2} \cdot \frac{2}{5} = -\frac{7}{2} \cdot \frac{2}{5} = -\frac{14}{10} = -\frac{7}{5} \)


11. \( \frac{1}{12} : ( -\frac{1}{4} ) = \frac{1}{12} \cdot (-4) = -\frac{4}{12} = -\frac{1}{3} \)


12. \( 7 \frac{18}{35} \)


13. \( 4 \frac{9}{10} \)


14. \( \frac{1}{2} - 1 = \frac{1}{2} - \frac{2}{2} = -\frac{1}{2} \)


15. \( 1 \frac{1}{2} \cdot 3 \frac{3}{5} = \frac{3}{2} \cdot \frac{18}{5} = \frac{54}{10} = \frac{27}{5} \)


16. \( 5 \frac{10}{12} \)


17. \( \frac{4}{9} \)


18. \( 2 \frac{7}{6} \)


19. \( 6 \frac{3}{4} \)


20. \( 2 \frac{5}{7} \)


21. \( 2 \frac{4}{33} \)


22. \( -3 \frac{2}{5} \cdot 2 \frac{1}{5} = -\frac{17}{5} \cdot \frac{11}{5} = -\frac{187}{25} \)


23. \( -4 \frac{5}{7} \cdot ( -2 \frac{6}{11} ) = -\frac{33}{7} \cdot ( -\frac{28}{11} ) = \frac{33}{7} \cdot \frac{28}{11} = 3 \cdot 4 = 12 \)


24. \( -7 \frac{3}{8} : ( -2 \frac{1}{16} ) = -\frac{67}{8} : ( -\frac{33}{16} ) = \frac{67}{8} \cdot \frac{16}{33} = \frac{67 \cdot 2}{33} = \frac{134}{33} \)


25. \( 4 \frac{1}{2} : 2 \frac{1}{5} = \frac{9}{2} : \frac{11}{5} = \frac{9}{2} \cdot \frac{5}{11} = \frac{45}{22} \)


26. \( -1 \frac{1}{3} : 1 \frac{1}{6} = -\frac{4}{3} : \frac{7}{6} = -\frac{4}{3} \cdot \frac{6}{7} = -\frac{24}{21} = -\frac{8}{7} \)


27. \( 1 \frac{1}{2} : 7 \frac{1}{25} = \frac{3}{2} : \frac{176}{25} = \frac{3}{2} \cdot \frac{25}{176} = \frac{75}{352} \)