Вопрос:

Вычислите: 1) 6\(\frac{4}{9}\) - 3\(\frac{5}{9}\); 2) 10\(\frac{11}{19}\) + 5\(\frac{14}{19}\); 3) 2\(\frac{3}{13}\) - 2\(\frac{11}{13}\); 4) 1\(\frac{5}{8}\) + 3\(\frac{7}{8}\); 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:

Решение:

  1. \( 6\frac{4}{9} - 3\frac{5}{9} = \frac{58}{9} - \frac{32}{9} = \frac{26}{9} = 2\frac{8}{9} \)
  2. \( 10\frac{11}{19} + 5\frac{14}{19} = 15\frac{25}{19} = 16\frac{6}{19} \)
  3. \( 2\frac{3}{13} - 2\frac{11}{13} = \frac{29}{13} - \frac{37}{13} = -\frac{8}{13} \)
  4. \( 1\frac{5}{8} + 3\frac{7}{8} = 4\frac{12}{8} = 5\frac{4}{8} = 5\frac{1}{2} \)
  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. \( 4 - 1\frac{4}{7} = 4 - \frac{11}{7} = \frac{28}{7} - \frac{11}{7} = \frac{17}{7} = 2\frac{3}{7} \)
  8. \( 10 - 9\frac{3}{10} = 10 - \frac{93}{10} = \frac{100}{10} - \frac{93}{10} = \frac{7}{10} \)
  9. \( 5\frac{2}{7} - 2\frac{5}{7} = \frac{37}{7} - \frac{19}{7} = \frac{18}{7} = 2\frac{4}{7} \)
  10. \( 14\frac{6}{20} - 8\frac{12}{20} = \frac{286}{20} - \frac{172}{20} = \frac{114}{20} = \frac{57}{10} = 5\frac{7}{10} \)
  11. \( 8\frac{3}{14} - 5\frac{9}{14} = \frac{115}{14} - \frac{79}{14} = \frac{36}{14} = \frac{18}{7} = 2\frac{4}{7} \)
  12. \( 7\frac{10}{21} - 4\frac{16}{21} = \frac{157}{21} - \frac{100}{21} = \frac{57}{21} = \frac{19}{7} = 2\frac{5}{7} \)
  13. \( 14\frac{8}{31} - 6\frac{8}{31} = \frac{442}{31} - \frac{194}{31} = \frac{248}{31} = 8 \)
  14. \( (12\frac{5}{22} + 7\frac{17}{22}) - (13\frac{7}{23} - 9\frac{15}{23}) = (19\frac{22}{22}) - (3\frac{25}{23}) = 20 - \frac{92}{23} = \frac{460}{23} - \frac{92}{23} = \frac{368}{23} = 16 \)

Ответ: 1) 2\(\frac{8}{9}\); 2) 16\(\frac{6}{19}\); 3) -\(\frac{8}{13}\); 4) 5\(\frac{1}{2}\); 5) \(\frac{8}{11}\); 6) \(\frac{27}{40}\); 7) 2\(\frac{3}{7}\); 8) \(\frac{7}{10}\); 9) 2\(\frac{4}{7}\); 10) 5\(\frac{7}{10}\); 11) 2\(\frac{4}{7}\); 12) 2\(\frac{5}{7}\); 13) 8; 14) 16.

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