Вопрос:

Выполнить действия с обыкновенными дробями: а) \(\frac{8}{15}\cdot4\); б) \(\frac{1}{5}+\frac{1}{3}\); в) \(\frac{1}{2}+\frac{3}{8}\); г) \(2\frac{3}{4}\cdot5\frac{7}{33}\); д) \(3\frac{3}{2}\); е) \(3\frac{3}{4}\); ж) \(-4\frac{2}{3}+7\frac{1}{2}\); з) \(-3\frac{1}{2}\cdot2\frac{2}{5}\); и) \(-1\frac{3}{4}\); к) \(-\frac{7}{12}:(-\frac{1}{4})\); л) \(\frac{1}{4}:2\); м) \(-\frac{7}{4}\cdot\frac{4}{9}\); н) \(6\frac{1}{2}-3\frac{3}{4}\); о) \(-\frac{4}{19}\cdot(-\frac{57}{64})\); п) \(-4\frac{2}{3}-7\frac{7}{9}\); р) \(3\frac{1}{3}+4\frac{1}{2}\); 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) \(2\frac{1}{2}-7\frac{5}{6}\); х) \(-4\frac{2}{3}-7\frac{7}{9}\); ц) \(4\frac{1}{3}\cdot2\frac{5}{6}\); ч) \(-7\frac{3}{8}\cdot(-2\frac{1}{16})\); ш) \(-1\frac{1}{3}:3\frac{1}{6}\); щ) \(4\frac{1}{5}:7\frac{1}{25}\).

Ответ:

  1. \(\frac{8}{15}\cdot4=\frac{32}{15}=2\frac{2}{15}\).
  2. \(\frac{1}{5}+\frac{1}{3}=\frac{3+5}{15}=\frac{8}{15}\).
  3. \(\frac{1}{2}+\frac{3}{8}=\frac{4}{8}+\frac{3}{8}=\frac{7}{8}\).
  4. \(2\frac{3}{4}\cdot5\frac{7}{33}=\frac{11}{4}\cdot\frac{172}{33}=\frac{43}{3}=14\frac{1}{3}\).
  5. \(3\frac{3}{2}=\frac{9}{2}=4\frac{1}{2}\).
  6. \(3\frac{3}{4}=\frac{15}{4}=3\frac{3}{4}\).
  7. \(-4\frac{2}{3}+7\frac{1}{2}=-\frac{14}{3}+\frac{15}{2}=\frac{17}{6}=2\frac{5}{6}\).
  8. \(-3\frac{1}{2}\cdot2\frac{2}{5}=-\frac{7}{2}\cdot\frac{12}{5}=-\frac{42}{5}=-8\frac{2}{5}\).
  9. \(-1\frac{3}{4}=-\frac{7}{4}\).
  10. \(-\frac{7}{12}:(-\frac{1}{4})=\frac{7}{12}\cdot4=\frac{7}{3}=2\frac{1}{3}\).
  11. \(\frac{1}{4}:2=\frac{1}{8}\).
  12. \(-\frac{7}{4}\cdot\frac{4}{9}=-\frac{7}{9}\).
  13. \(6\frac{1}{2}-3\frac{3}{4}=\frac{13}{2}-\frac{15}{4}=\frac{11}{4}=2\frac{3}{4}\).
  14. \(-\frac{4}{19}\cdot(-\frac{57}{64})=\frac{3}{16}\).
  15. \(-4\frac{2}{3}-7\frac{7}{9}=-\frac{14}{3}-\frac{70}{9}=-\frac{112}{9}=-12\frac{4}{9}\).
  16. \(3\frac{1}{3}+4\frac{1}{2}=\frac{10}{3}+\frac{9}{2}=\frac{47}{6}=7\frac{5}{6}\).
  17. \(4\frac{1}{3}+\frac{3}{17}=\frac{13}{3}+\frac{3}{17}=\frac{230}{51}=4\frac{26}{51}\).
  18. \(-5\frac{2}{5}+4\frac{1}{3}=-\frac{27}{5}+\frac{13}{3}=-\frac{16}{15}=-1\frac{1}{15}\).
  19. \(6\frac{1}{2}-3\frac{3}{4}=2\frac{3}{4}\).
  20. \(2\frac{1}{2}-7\frac{5}{6}=\frac{5}{2}-\frac{47}{6}=-\frac{16}{3}=-5\frac{1}{3}\).
  21. \(-4\frac{2}{3}-7\frac{7}{9}=-12\frac{4}{9}\).
  22. \(4\frac{1}{3}\cdot2\frac{5}{6}=\frac{13}{3}\cdot\frac{17}{6}=\frac{221}{18}=12\frac{5}{18}\).
  23. \(-7\frac{3}{8}\cdot(-2\frac{1}{16})=-\frac{59}{8}\cdot(-\frac{33}{16})=\frac{1947}{128}=15\frac{27}{128}\).
  24. \(-1\frac{1}{3}:3\frac{1}{6}=-\frac{4}{3}:\frac{19}{6}=-\frac{8}{19}\).
  25. \(4\frac{1}{5}:7\frac{1}{25}=\frac{21}{5}:\frac{176}{25}=\frac{15}{8}=1\frac{7}{8}\).

Ответ: \(2\frac{2}{15};\ \frac{8}{15};\ \frac{7}{8};\ 14\frac{1}{3};\ 4\frac{1}{2};\ 3\frac{3}{4};\ 2\frac{5}{6};\ -8\frac{2}{5};\ -\frac{7}{4};\ 2\frac{1}{3};\ \frac{1}{8};\ -\frac{7}{9};\ 2\frac{3}{4};\ \frac{3}{16};\ -12\frac{4}{9};\ 7\frac{5}{6};\ 4\frac{26}{51};\ -1\frac{1}{15};\ 2\frac{3}{4};\ -5\frac{1}{3};\ -12\frac{4}{9};\ 12\frac{5}{18};\ 15\frac{27}{128};\ -\frac{8}{19};\ 1\frac{7}{8}\).

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