Контрольные задания > Выполните действия: a) 1 1/3 : (8 2/3 : 1 4/9 - 3 3/8 + 1 5/8) - 1 5/6; б) (3 1/15 - 1 1/15 : 1 3/5 + 2/5) * 2 1/7 - 1 1/7; в) 19,6 * 2 1/2 - (2,0625 - 1 5/12) : 1/8; г) 5/16 : 0,125 + 1,456 : 7/25 + 4,5 * 4/5.
Вопрос:

Выполните действия: a) 1 1/3 : (8 2/3 : 1 4/9 - 3 3/8 + 1 5/8) - 1 5/6; б) (3 1/15 - 1 1/15 : 1 3/5 + 2/5) * 2 1/7 - 1 1/7; в) 19,6 * 2 1/2 - (2,0625 - 1 5/12) : 1/8; г) 5/16 : 0,125 + 1,456 : 7/25 + 4,5 * 4/5.

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Ответ:

Решение:



  1. а) \( 1\frac{1}{3} : \left( 8\frac{2}{3} : 1\frac{4}{9} - 3\frac{3}{8} + 1\frac{5}{8} \right) - 1\frac{5}{6} \)

  2. \( 8\frac{2}{3} = \frac{26}{3} \), \( 1\frac{4}{9} = \frac{13}{9} \), \( 3\frac{3}{8} = \frac{27}{8} \), \( 1\frac{5}{8} = \frac{13}{8} \), \( 1\frac{5}{6} = \frac{11}{6} \), \( 1\frac{1}{3} = \frac{4}{3} \)

  3. \( 8\frac{2}{3} : 1\frac{4}{9} = \frac{26}{3} : \frac{13}{9} = \frac{26}{3} \cdot \frac{9}{13} = 2 \cdot 3 = 6 \)

  4. \( 6 - 3\frac{3}{8} + 1\frac{5}{8} = 6 - \frac{27}{8} + \frac{13}{8} = 6 + \frac{13 - 27}{8} = 6 + \frac{-14}{8} = 6 - \frac{7}{4} = \frac{24 - 7}{4} = \frac{17}{4} \)

  5. \( 1\frac{1}{3} : \frac{17}{4} - 1\frac{5}{6} = \frac{4}{3} : \frac{17}{4} - \frac{11}{6} = \frac{4}{3} \cdot \frac{4}{17} - \frac{11}{6} = \frac{16}{51} - \frac{11}{6} = \frac{16 \cdot 2 - 11 \cdot 17}{102} = \frac{32 - 187}{102} = \frac{-155}{102} = -1\frac{53}{102} \)

  6. б) \( \left( 3\frac{1}{15} - 1\frac{1}{15} : 1\frac{3}{5} + \frac{2}{5} \right) \cdot 2\frac{1}{7} - 1\frac{1}{7} \)

  7. \( 3\frac{1}{15} = \frac{46}{15} \), \( 1\frac{1}{15} = \frac{16}{15} \), \( 1\frac{3}{5} = \frac{8}{5} \), \( 2\frac{1}{7} = \frac{15}{7} \), \( 1\frac{1}{7} = \frac{8}{7} \)

  8. \( 1\frac{1}{15} : 1\frac{3}{5} = \frac{16}{15} : \frac{8}{5} = \frac{16}{15} \cdot \frac{5}{8} = \frac{2}{3} \)

  9. \( \frac{46}{15} - \frac{2}{3} + \frac{2}{5} = \frac{46 - 10 + 6}{15} = \frac{42}{15} = \frac{14}{5} \)

  10. \( \frac{14}{5} \cdot \frac{15}{7} - \frac{8}{7} = 2 \cdot 3 - \frac{8}{7} = 6 - \frac{8}{7} = \frac{42 - 8}{7} = \frac{34}{7} = 4\frac{6}{7} \)

  11. в) \( 19,6 \cdot 2\frac{1}{2} - \left( 2,0625 - 1\frac{5}{12} \right) : \frac{1}{8} \)

  12. \( 19,6 = \frac{196}{10} = \frac{98}{5} \), \( 2\frac{1}{2} = \frac{5}{2} \), \( 2,0625 = 2\frac{1}{16} = \frac{33}{16} \), \( 1\frac{5}{12} = \frac{17}{12} \)

  13. \( 19,6 \cdot 2\frac{1}{2} = \frac{98}{5} \cdot \frac{5}{2} = 49 \)

  14. \( 2,0625 - 1\frac{5}{12} = \frac{33}{16} - \frac{17}{12} = \frac{33 \cdot 3 - 17 \cdot 4}{48} = \frac{99 - 68}{48} = \frac{31}{48} \)

  15. \( \frac{31}{48} : \frac{1}{8} = \frac{31}{48} \cdot 8 = \frac{31}{6} \)

  16. \( 49 - \frac{31}{6} = \frac{49 \cdot 6 - 31}{6} = \frac{294 - 31}{6} = \frac{263}{6} = 43\frac{5}{6} \)

  17. г) \( \frac{5}{16} : 0,125 + 1,456 : \frac{7}{25} + 4,5 \cdot \frac{4}{5} \)

  18. \( 0,125 = \frac{1}{8} \), \( 1,456 = \frac{1456}{1000} = \frac{182}{125} \), \( 4,5 = \frac{45}{10} = \frac{9}{2} \)

  19. \( \frac{5}{16} : \frac{1}{8} = \frac{5}{16} \cdot 8 = \frac{5}{2} \)

  20. \( 1,456 : \frac{7}{25} = \frac{182}{125} : \frac{7}{25} = \frac{182}{125} \cdot \frac{25}{7} = \frac{182 \cdot 1}{5 \cdot 7} = \frac{26 \cdot 1}{5 \cdot 1} = \frac{26}{5} \)

  21. \( 4,5 \cdot \frac{4}{5} = \frac{9}{2} \cdot \frac{4}{5} = \frac{9 \cdot 2}{5} = \frac{18}{5} \)

  22. \( \frac{5}{2} + \frac{26}{5} + \frac{18}{5} = \frac{5}{2} + \frac{44}{5} = \frac{5 \cdot 5 + 44 \cdot 2}{10} = \frac{25 + 88}{10} = \frac{113}{10} = 11,3 \)


Ответ: а) -1 53/102; б) 4 6/7; в) 43 5/6; г) 11,3.

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