Вопрос:

9. Найти значение выражений: а) \((-15,64:4\frac{3}{5}+7,1)\cdot2\frac{2}{5}\); б) \((0,4-\frac{11}{15})\cdot1\frac{2}{7}-\left(\frac{7}{18}-0,5\right):1\frac{1}{6}\); в) \(0,8:\frac{37,12-5,6\cdot0,14}{1,21+3,4\cdot0,35}\); г) \((2,17\cdot3,7-1,83\cdot2,3):19,1\); д) \(5\frac{4}{19}\cdot3\frac{2}{7}+1\frac{15}{19}:\frac{7}{25}-1\frac{2}{3}\); е) \(\frac{(3\frac{1}{3}-2\frac{2}{3})\cdot2,4}{(15,5+4,5):2\frac{1}{2}}\cdot5\frac{3}{7}-(2\frac{1}{2}+1\frac{1}{3}):\frac{1}{6}\); ж) \((2\frac{7}{15}+1\frac{7}{12})\cdot1\frac{1}{9}-1\frac{7}{8}\); з) \((6\frac{1}{7}-5\frac{3}{4}):\frac{11}{14}+(3\frac{3}{4}-1\frac{5}{6}):\frac{1}{6}\).

Ответ:

  1. а) \(-15,64:4\frac{3}{5}+7,1=-3,4+7,1=3,7\); \(3,7\cdot2\frac{2}{5}=3,7\cdot2,4=8,88\).
  2. б) \((0,4-\frac{11}{15})\cdot1\frac{2}{7}-\left(\frac{7}{18}-0,5\right):1\frac{1}{6}=\left(\frac25-\frac{11}{15}\right)\cdot\frac97-\left(\frac7{18}-\frac12\right):\frac76=-\frac13\cdot\frac97-\left(-\frac29\right)\cdot\frac67=-\frac37+\frac4{21}=-\frac5{21}\).
  3. в) \(0,8:\frac{37,12-5,6\cdot0,14}{1,21+3,4\cdot0,35}=0,8:\frac{36,336}{2,4}=0,8:15,14=\frac4{75}\).
  4. г) \((2,17\cdot3,7-1,83\cdot2,3):19,1=(8,029-4,209):19,1=3,82:19,1=0,2\).
  5. д) \(5\frac4{19}\cdot3\frac27+1\frac{15}{19}:\frac7{25}-1\frac23=\frac{99}{19}\cdot\frac{23}{7}+\frac{34}{19}\cdot\frac{25}{7}-\frac53=\frac{2277+850}{133}-\frac53=\frac{3127}{133}-\frac{665}{399}=\frac{8726}{399}\).
  6. е) \(\frac{(3\frac13-2\frac23)\cdot2,4}{(15,5+4,5):2\frac12}\cdot5\frac37-(2\frac12+1\frac13):\frac16=\frac{\frac23\cdot\frac{12}{5}}{20: \frac52}\cdot\frac{38}{7}-\frac{23}{6}\cdot6=\frac{8}{25}\cdot\frac{38}{7}-23=\frac{304}{175}-23=-\frac{3721}{175}\).
  7. ж) \(\left(2\frac7{15}+1\frac7{12}\right)\cdot1\frac19-1\frac78=\left(\frac{37}{15}+\frac{19}{12}\right)\cdot\frac{10}{9}-\frac{15}{8}=\frac{239}{60}\cdot\frac{10}{9}-\frac{15}{8}=\frac{239}{54}-\frac{15}{8}=\frac{557}{216}\).
  8. з) \((6\frac17-5\frac34):\frac{11}{14}+(3\frac34-1\frac56):\frac16=\left(\frac{43}{7}-\frac{23}{4}\right)\cdot\frac{14}{11}+\left(\frac{15}{4}-\frac{11}{6}\right)\cdot6=\frac{27}{44}+\frac{23}{2}=\frac{533}{44}\).

Ответ: а) 8,88; б) \(-\frac5{21}\); в) \(\frac4{75}\); г) 0,2; д) \(\frac{8726}{399}\); е) \(-\frac{3721}{175}\); ж) \(\frac{557}{216}\); з) \(\frac{533}{44}\).

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