Вопрос:

Вычислите: 1) $$6\frac{4}{7}+3\frac{5}{7}$$; 2) $$10\frac{11}{19}+5\frac{14}{19}$$; 3) $$2\frac{3}{13}+2\frac{11}{13}$$; 4) $$1\frac{5}{8}+3\frac{3}{8}$$; 5) $$1-\frac{3}{11}$$; 6) $$1-\frac{13}{40}$$; 7) $$4-1\frac{4}{7}$$; 8) $$10-9\frac{3}{10}$$; 9) $$5\frac{2}{7}-2\frac{5}{7}$$; 10) $$14\frac{6}{20}-8\frac{12}{20}$$; 11) $$8\frac{3}{14}-5\frac{9}{14}$$; 12) $$7\frac{10}{21}-4\frac{16}{21}$$; 13) $$14\frac{8}{31}-6\frac{8}{31}$$; 14) $$(12\frac{5}{22}+7\frac{17}{22})-(13\frac{7}{23}-9\frac{15}{23})$$.

Ответ:

Вычислите:

  1. $$6\frac{4}{7}+3\frac{5}{7} = 9 + \frac{4}{7} + \frac{5}{7} = 9 + \frac{9}{7} = 9 + 1\frac{2}{7} = 10\frac{2}{7}$$
  2. $$10\frac{11}{19}+5\frac{14}{19} = 15 + \frac{11}{19} + \frac{14}{19} = 15 + \frac{25}{19} = 15 + 1\frac{6}{19} = 16\frac{6}{19}$$
  3. $$2\frac{3}{13}+2\frac{11}{13} = 4 + \frac{3}{13} + \frac{11}{13} = 4 + \frac{14}{13} = 4 + 1\frac{1}{13} = 5\frac{1}{13}$$
  4. $$1\frac{5}{8}+3\frac{3}{8} = 4 + \frac{5}{8} + \frac{3}{8} = 4 + \frac{8}{8} = 4 + 1 = 5$$
  5. $$1-\frac{3}{11} = \frac{11}{11} - \frac{3}{11} = \frac{8}{11}$$
  6. $$1-\frac{13}{40} = \frac{40}{40} - \frac{13}{40} = \frac{27}{40}$$
  7. $$4-1\frac{4}{7} = 3\frac{7}{7} - 1\frac{4}{7} = 2\frac{3}{7}$$
  8. $$10-9\frac{3}{10} = 9\frac{10}{10} - 9\frac{3}{10} = \frac{7}{10}$$
  9. $$5\frac{2}{7}-2\frac{5}{7} = 4\frac{9}{7}-2\frac{5}{7} = 2\frac{4}{7}$$
  10. $$14\frac{6}{20}-8\frac{12}{20} = 13\frac{26}{20}-8\frac{12}{20} = 5\frac{14}{20} = 5\frac{7}{10}$$
  11. $$8\frac{3}{14}-5\frac{9}{14} = 7\frac{17}{14}-5\frac{9}{14} = 2\frac{8}{14} = 2\frac{4}{7}$$
  12. $$7\frac{10}{21}-4\frac{16}{21} = 6\frac{31}{21}-4\frac{16}{21} = 2\frac{15}{21} = 2\frac{5}{7}$$
  13. $$14\frac{8}{31}-6\frac{8}{31} = 8$$
  14. $$(12\frac{5}{22}+7\frac{17}{22})-(13\frac{7}{23}-9\frac{15}{23}) = (19 + \frac{5}{22} + \frac{17}{22}) - (4 + \frac{7}{23} - \frac{15}{23}) = (19 + \frac{22}{22}) - (4 - \frac{8}{23}) = 20 - 4 + \frac{8}{23} = 16\frac{8}{23}$$
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