Найдите значение выражения.

Образец:

\( 1\frac{1}{2} + 2\frac{2}{3} = (1+2) + (\frac{1}{2} + \frac{2}{3}) = 3 + (\frac{3}{6} + \frac{4}{6}) = 3 + \frac{7}{6} = 3 + 1\frac{1}{6} = 4\frac{1}{6} \)

Решение:

1. а) \( 3\frac{3}{11} + 3\frac{5}{15} \)
   \( 3\frac{3}{11} + 3\frac{5}{15} = (3+3) + (\frac{3}{11} + \frac{5}{15}) = 6 + (\frac{45}{165} + \frac{55}{165}) = 6 + \frac{100}{165} = 6 + \frac{20}{33} = 6\frac{20}{33} \)
2. б) \( 3\frac{7}{3} + 8\frac{15}{4} \)
   \( 3\frac{7}{3} + 8\frac{15}{4} = (3+8) + (\frac{7}{3} + \frac{15}{4}) = 11 + (\frac{28}{12} + \frac{45}{12}) = 11 + \frac{73}{12} = 11 + 6\frac{1}{12} = 17\frac{1}{12} \)
3. в) \( 4\frac{3}{4} + 5\frac{4}{5} \)
   \( 4\frac{3}{4} + 5\frac{4}{5} = (4+5) + (\frac{3}{4} + \frac{4}{5}) = 9 + (\frac{15}{20} + \frac{16}{20}) = 9 + \frac{31}{20} = 9 + 1\frac{11}{20} = 10\frac{11}{20} \)
4. г) \( 4\frac{4}{9} + 5\frac{15}{4} \)
   \( 4\frac{4}{9} + 5\frac{15}{4} = (4+5) + (\frac{4}{9} + \frac{15}{4}) = 9 + (\frac{16}{36} + \frac{135}{36}) = 9 + \frac{151}{36} = 9 + 4\frac{7}{36} = 13\frac{7}{36} \)
5. д) \( 5\frac{7}{12} + 3\frac{4}{3} \)
   \( 5\frac{7}{12} + 3\frac{4}{3} = (5+3) + (\frac{7}{12} + \frac{4}{3}) = 8 + (\frac{7}{12} + \frac{16}{12}) = 8 + \frac{23}{12} = 8 + 1\frac{11}{12} = 9\frac{11}{12} \)
6. е) \( 3\frac{3}{8} + 5\frac{8}{12} \)
   \( 3\frac{3}{8} + 5\frac{8}{12} = (3+5) + (\frac{3}{8} + \frac{8}{12}) = 8 + (\frac{9}{24} + \frac{16}{24}) = 8 + \frac{25}{24} = 8 + 1\frac{1}{24} = 9\frac{1}{24} \)
7. ж) \( 8\frac{8}{3} + 3\frac{10}{15} \)
   \( 8\frac{8}{3} + 3\frac{10}{15} = (8+3) + (\frac{8}{3} + \frac{10}{15}) = 11 + (\frac{40}{15} + \frac{10}{15}) = 11 + \frac{50}{15} = 11 + 3\frac{5}{15} = 11 + 3\frac{1}{3} = 14\frac{1}{3} \)
8. и) \( 3\frac{5}{6} + 1\frac{21}{7} \)
   \( 3\frac{5}{6} + 1\frac{21}{7} = (3+1) + (\frac{5}{6} + \frac{21}{7}) = 4 + (\frac{35}{42} + \frac{126}{42}) = 4 + \frac{161}{42} = 4 + 3\frac{35}{42} = 4 + 3\frac{5}{6} = 7\frac{5}{6} \)
9. к) \( 2\frac{1}{7} + 5\frac{13}{6} \)
   \( 2\frac{1}{7} + 5\frac{13}{6} = (2+5) + (\frac{1}{7} + \frac{13}{6}) = 7 + (\frac{6}{42} + \frac{91}{42}) = 7 + \frac{97}{42} = 7 + 2\frac{13}{42} = 9\frac{13}{42} \)
10. л) \( 1\frac{17}{12} + 3\frac{51}{51} \)
    \( 1\frac{17}{12} + 3\frac{51}{51} = 1\frac{17}{12} + 3 + 1 = 5\frac{17}{12} = 5 + 1\frac{5}{12} = 6\frac{5}{12} \)

Ответ: а) \( 6\frac{20}{33} \); б) \( 17\frac{1}{12} \); в) \( 10\frac{11}{20} \); г) \( 13\frac{7}{36} \); д) \( 9\frac{11}{12} \); е) \( 9\frac{1}{24} \); ж) \( 14\frac{1}{3} \); и) \( 7\frac{5}{6} \); к) \( 9\frac{13}{42} \); л) \( 6\frac{5}{12} \).