Вопрос:

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

Ответ:

  1. $$10\frac{11}{19} + 5\frac{4}{19} = (10 + 5) + (\frac{11}{19} + \frac{4}{19}) = 15 + \frac{15}{19} = 15\frac{15}{19}$$

    Ответ: $$15\frac{15}{19}$$

  2. $$2\frac{3}{13} + 2\frac{11}{13} = (2 + 2) + (\frac{3}{13} + \frac{11}{13}) = 4 + \frac{14}{13} = 4 + 1\frac{1}{13} = 5\frac{1}{13}$$

    Ответ: $$5\frac{1}{13}$$

  3. $$1\frac{5}{8} + 3\frac{7}{8} = (1 + 3) + (\frac{5}{8} + \frac{7}{8}) = 4 + \frac{12}{8} = 4 + 1\frac{4}{8} = 5\frac{4}{8} = 5\frac{1}{2}$$

    Ответ: $$5\frac{1}{2}$$

  4. $$1 - \frac{3}{11} = \frac{11}{11} - \frac{3}{11} = \frac{8}{11}$$

    Ответ: $$\frac{8}{11}$$

  5. $$1 - \frac{13}{40} = \frac{40}{40} - \frac{13}{40} = \frac{27}{40}$$

    Ответ: $$\frac{27}{40}$$

  6. $$4 - 1\frac{4}{7} = 4 - \frac{11}{7} = \frac{28}{7} - \frac{11}{7} = \frac{17}{7} = 2\frac{3}{7}$$

    Ответ: $$2\frac{3}{7}$$

  7. $$10 - 9\frac{3}{10} = 10 - \frac{93}{10} = \frac{100}{10} - \frac{93}{10} = \frac{7}{10}$$

    Ответ: $$\frac{7}{10}$$

  8. $$5\frac{2}{7} - 2\frac{5}{7} = \frac{37}{7} - \frac{19}{7} = \frac{18}{7} = 2\frac{4}{7}$$

    Ответ: $$2\frac{4}{7}$$

  9. $$14\frac{6}{20} - 8\frac{12}{20} = 14\frac{3}{10} - 8\frac{6}{10} = \frac{143}{10} - \frac{86}{10} = \frac{57}{10} = 5\frac{7}{10}$$

    Ответ: $$5\frac{7}{10}$$

  10. $$8\frac{3}{14} - 5\frac{9}{14} = \frac{115}{14} - \frac{79}{14} = \frac{36}{14} = \frac{18}{7} = 2\frac{4}{7}$$

    Ответ: $$2\frac{4}{7}$$

  11. $$7\frac{10}{21} - 4\frac{16}{21} = \frac{157}{21} - \frac{100}{21} = \frac{57}{21} = \frac{19}{7} = 2\frac{5}{7}$$

    Ответ: $$2\frac{5}{7}$$

  12. $$14\frac{8}{31} - 6\frac{8}{31} = (14 - 6) + (\frac{8}{31} - \frac{8}{31}) = 8 + 0 = 8$$

    Ответ: $$8$$

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