Контрольные задания > 6. 1) (20\frac{8}{15} - 7\frac{1}{2} - 54\frac{3}{5} : 2\frac{1}{2}):(\frac{13}{21} \cdot 8\frac{2}{5} - 29\frac{6}{5}) - 1\frac{5}{6} + \frac{1}{6} + \frac{21}{26} 2) 9\frac{7}{7} \cdot 1\frac{2}{7} + 43\frac{3}{4} : 11\frac{2}{3} - 3\frac{18}{25} + 1\frac{1}{45} - (37\frac{1}{2} : 2\frac{1}{12} - 1\frac{1}{23} \cdot 9) + \frac{47}{100}
Вопрос:

6. 1) (20\frac{8}{15} - 7\frac{1}{2} - 54\frac{3}{5} : 2\frac{1}{2}):(\frac{13}{21} \cdot 8\frac{2}{5} - 29\frac{6}{5}) - 1\frac{5}{6} + \frac{1}{6} + \frac{21}{26} 2) 9\frac{7}{7} \cdot 1\frac{2}{7} + 43\frac{3}{4} : 11\frac{2}{3} - 3\frac{18}{25} + 1\frac{1}{45} - (37\frac{1}{2} : 2\frac{1}{12} - 1\frac{1}{23} \cdot 9) + \frac{47}{100}

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Ответ:

Решим примеры по действиям:
  1. 20\frac{8}{15} - 7\frac{1}{2} = \frac{308}{15} - \frac{15}{2} = \frac{616 - 225}{30} = \frac{391}{30} = 13\frac{1}{30}
  2. 54\frac{3}{5} : 2\frac{1}{2} = \frac{273}{5} : \frac{5}{2} = \frac{273 \cdot 2}{5 \cdot 5} = \frac{546}{25} = 21\frac{21}{25}
  3. 13\frac{1}{30} - 21\frac{21}{25} = \frac{391}{30} - \frac{546}{25} = \frac{391 \cdot 5 - 546 \cdot 6}{150} = \frac{1955 - 3276}{150} = \frac{-1321}{150} = -8\frac{14}{150} = -8\frac{7}{75}
  4. \frac{13}{21} \cdot 8\frac{2}{5} = \frac{13}{21} \cdot \frac{42}{5} = \frac{13 \cdot 42}{21 \cdot 5} = \frac{13 \cdot 2}{5} = \frac{26}{5} = 5\frac{1}{5}
  5. 5\frac{1}{5} - 29\frac{6}{5} = \frac{26}{5} - \frac{146}{5} = \frac{26 - 146}{5} = \frac{-120}{5} = -24
  6. -8\frac{7}{75} : (-24) = -\frac{607}{75} : (-24) = \frac{607}{75 \cdot 24} = \frac{607}{1800}
  7. 1\frac{5}{6} + \frac{1}{6} = \frac{11}{6} + \frac{1}{6} = \frac{12}{6} = 2
  8. \frac{607}{1800} - 2 + \frac{21}{26} = \frac{607}{1800} - \frac{3600}{1800} + \frac{21}{26} = \frac{-2993}{1800} + \frac{21}{26} = \frac{-2993 \cdot 13 + 21 \cdot 900}{23400} = \frac{-38909 + 18900}{23400} = \frac{-20009}{23400}
  1. 9\frac{7}{7} = 10
  2. 1\frac{2}{7} = \frac{9}{7}
  3. 10 \cdot \frac{9}{7} = \frac{90}{7} = 12\frac{6}{7}
  4. 43\frac{3}{4} : 11\frac{2}{3} = \frac{175}{4} : \frac{35}{3} = \frac{175 \cdot 3}{4 \cdot 35} = \frac{5 \cdot 3}{4} = \frac{15}{4} = 3\frac{3}{4}
  5. 12\frac{6}{7} + 3\frac{3}{4} = \frac{90}{7} + \frac{15}{4} = \frac{90 \cdot 4 + 15 \cdot 7}{28} = \frac{360 + 105}{28} = \frac{465}{28} = 16\frac{17}{28}
  6. 16\frac{17}{28} - 3\frac{18}{25} = \frac{465}{28} - \frac{93}{25} = \frac{465 \cdot 25 - 93 \cdot 28}{700} = \frac{11625 - 2604}{700} = \frac{9021}{700} = 12\frac{621}{700}
  7. 12\frac{621}{700} + 1\frac{1}{45} = \frac{9021}{700} + \frac{46}{45} = \frac{9021 \cdot 9 + 46 \cdot 140}{6300} = \frac{81189 + 6440}{6300} = \frac{87629}{6300}
  8. 37\frac{1}{2} : 2\frac{1}{12} = \frac{75}{2} : \frac{25}{12} = \frac{75 \cdot 12}{2 \cdot 25} = \frac{3 \cdot 6}{1} = 18
  9. 1\frac{1}{23} \cdot 9 = \frac{24 \cdot 9}{23} = \frac{216}{23} = 9\frac{9}{23}
  10. 18 - 9\frac{9}{23} = \frac{18}{1} - \frac{216}{23} = \frac{18 \cdot 23 - 216}{23} = \frac{414 - 216}{23} = \frac{198}{23} = 8\frac{14}{23}
  11. \frac{87629}{6300} - 8\frac{14}{23} = \frac{87629}{6300} - \frac{198}{23} = \frac{87629 \cdot 23 - 198 \cdot 6300}{144900} = \frac{2015467 - 1247400}{144900} = \frac{768067}{144900} + \frac{47}{100}
  12. \frac{768067}{144900} + \frac{47}{100} = \frac{76806700 + 47 \cdot 144900}{14490000} = \frac{76806700 + 6810300}{14490000} = \frac{83617000}{14490000} = 5\frac{11167}{14490}

Ответ: \frac{-20009}{23400} ; 5\frac{11167}{14490}

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