Вопрос:
Вычислите: 1) \((3\frac12-2\frac23+5\frac56+4\frac35)\cdot24\); 2) \((5\frac38+18\frac12-7\frac5{24}):16\frac23\); 3) \((12\frac5{12}+1\frac23-3\frac56+2\frac34):(2\frac12\cdot\frac25-\frac79)\); 4) \(48\frac35:6\frac34\cdot\frac5{12}-2\frac56+1\frac{75}{94}\cdot(1\frac12\cdot\frac13-13:26)\).
Ответ:
- \[(3\frac12-2\frac23+5\frac56+4\frac35)\cdot24=\left(\frac72-\frac83+\frac{35}{6}+\frac{23}{5}\right)\cdot24=\frac{389}{30}\cdot24=\frac{1556}{5}=311\frac15.\]
- \[(5\frac38+18\frac12-7\frac5{24}):16\frac23=\left(\frac{43}{8}+\frac{37}{2}-\frac{173}{24}\right):\frac{50}{3}=\frac{79}{3}\cdot\frac{3}{50}=\frac{79}{50}=1\frac{29}{50}.\]
- \[(12\frac5{12}+1\frac23-3\frac56+2\frac34):(2\frac12\cdot\frac25-\frac79)=\left(\frac{149}{12}+\frac53-\frac{23}{6}+\frac{11}{4}\right):\left(1-\frac79\right)=\frac{44}{3}:\frac29=66.\]
- \[48\frac35:6\frac34\cdot\frac5{12}-2\frac56+1\frac{75}{94}\cdot(1\frac12\cdot\frac13-13:26)=\frac{243}{5}:\frac{27}{4}\cdot\frac5{12}-\frac{17}{6}+\frac{169}{94}\cdot\left(\frac12-\frac12\right)=6-\frac{17}{6}=\frac{19}{6}=3\frac16.\]
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