2. Выполнить действия с дробями: а) \( \frac{1}{5} + \frac{1}{3} \) б) \( \frac{1}{2} + \frac{3}{8} \) в) \( \frac{3}{4} + 2 \) г) \( \frac{2}{3} - \frac{1}{6} \) д) \( \frac{7}{12} - 1 \) е) \( \frac{4}{5} - \frac{9}{10} \) з) \( \frac{8}{15} : 4 \) и) \( 3 : \frac{3}{2} \) й) \( -1 : \frac{3}{4} \) к) \( -\frac{7}{12} : \left( -\frac{1}{4} \right) \) л) \( \frac{1}{4} \cdot 2 \) м) \( -\frac{3}{4} \cdot \frac{4}{9} \) п) \( 2\frac{3}{4} + 3\frac{5}{7} \) р) \( -4\frac{2}{3} + 7\frac{1}{2} \) с) \( 4\frac{1}{3} + \frac{3}{17} \) т) \( -5\frac{2}{5} + 4\frac{1}{3} \) у) \( 6\frac{1}{2} - 3\frac{3}{4} \) ф) \( 2\frac{1}{2} - 7\frac{5}{6} \) ч) \( 2\frac{3}{4} \cdot 5\frac{7}{33} \) ь) \( -3\frac{1}{2} \cdot 2\frac{2}{7} \) ю) \( 4\frac{1}{5} : 7\frac{1}{25} \)

Решение:

1. а) \( \frac{1}{5} + \frac{1}{3} = \frac{3+5}{15} = \frac{8}{15} \)
2. б) \( \frac{1}{2} + \frac{3}{8} = \frac{4+3}{8} = \frac{7}{8} \)
3. в) \( \frac{3}{4} + 2 = \frac{3+8}{4} = \frac{11}{4} \)
4. г) \( \frac{2}{3} - \frac{1}{6} = \frac{4-1}{6} = \frac{3}{6} = \frac{1}{2} \)
5. д) \( \frac{7}{12} - 1 = \frac{7-12}{12} = -\frac{5}{12} \)
6. е) \( \frac{4}{5} - \frac{9}{10} = \frac{8-9}{10} = -\frac{1}{10} \)
7. з) \( \frac{8}{15} : 4 = \frac{8}{15 \cdot 4} = \frac{2}{15} \)
8. и) \( 3 : \frac{3}{2} = 3 \cdot \frac{2}{3} = 2 \)
9. й) \( -1 : \frac{3}{4} = -1 \cdot \frac{4}{3} = -\frac{4}{3} \)
10. к) \( -\frac{7}{12} : \left( -\frac{1}{4} \right) = \frac{7}{12} \cdot \frac{4}{1} = \frac{7}{3} \)
11. л) \( \frac{1}{4} \cdot 2 = \frac{2}{4} = \frac{1}{2} \)
12. м) \( -\frac{3}{4} \cdot \frac{4}{9} = -\frac{3 \cdot 4}{4 \cdot 9} = -\frac{1}{3} \)
13. п) \( 2\frac{3}{4} + 3\frac{5}{7} = \frac{11}{4} + \frac{26}{7} = \frac{77+104}{28} = \frac{181}{28} = 6\frac{13}{28} \)
14. р) \( -4\frac{2}{3} + 7\frac{1}{2} = -\frac{14}{3} + \frac{15}{2} = \frac{-28+45}{6} = \frac{17}{6} = 2\frac{5}{6} \)
15. с) \( 4\frac{1}{3} + \frac{3}{17} = \frac{13}{3} + \frac{3}{17} = \frac{13 \cdot 17 + 3 \cdot 3}{51} = \frac{221+9}{51} = \frac{230}{51} = 4\frac{26}{51} \)
16. т) \( -5\frac{2}{5} + 4\frac{1}{3} = -\frac{27}{5} + \frac{13}{3} = \frac{-81+65}{15} = -\frac{16}{15} = -1\frac{1}{15} \)
17. у) \( 6\frac{1}{2} - 3\frac{3}{4} = \frac{13}{2} - \frac{15}{4} = \frac{26-15}{4} = \frac{11}{4} = 2\frac{3}{4} \)
18. ф) \( 2\frac{1}{2} - 7\frac{5}{6} = \frac{5}{2} - \frac{47}{6} = \frac{15-47}{6} = -\frac{32}{6} = -\frac{16}{3} = -5\frac{1}{3} \)
19. ч) \( 2\frac{3}{4} \cdot 5\frac{7}{33} = \frac{11}{4} \cdot \frac{172}{33} = \frac{11 \cdot 172}{4 \cdot 33} = \frac{172}{4 \cdot 3} = \frac{43}{3} = 14\frac{1}{3} \)
20. ь) \( -3\frac{1}{2} \cdot 2\frac{2}{7} = -\frac{7}{2} \cdot \frac{16}{7} = -\frac{7 \cdot 16}{2 \cdot 7} = -8 \)
21. ю) \( 4\frac{1}{5} : 7\frac{1}{25} = \frac{21}{5} : \frac{176}{25} = \frac{21}{5} \cdot \frac{25}{176} = \frac{21 \cdot 5}{176} = \frac{105}{176} \)

Ответ: \( \frac{8}{15} \); \( \frac{7}{8} \); \( \frac{11}{4} \); \( \frac{1}{2} \); \( -\frac{5}{12} \); \( -\frac{1}{10} \); \( \frac{2}{15} \); 2; \( -\frac{4}{3} \); \( \frac{7}{3} \); \( \frac{1}{2} \); \( -\frac{1}{3} \); \( 6\frac{13}{28} \); \( 2\frac{5}{6} \); \( 4\frac{26}{51} \); \( -1\frac{1}{15} \); \( 2\frac{3}{4} \); \( -5\frac{1}{3} \); \( 14\frac{1}{3} \); -8; \( \frac{105}{176} \).