Вопрос:

Вычислите: 1) \(2:\frac{3}{5}+\frac{3}{5}:2+1\frac{1}{2}:6+6:1\frac{1}{2}\); 2) \(6\frac{1}{4}\cdot8-3\frac{2}{3}\cdot5\frac{1}{2}+2\frac{2}{5}\cdot4\frac{7}{12}\); 3) \(2\frac{1}{2}\cdot48-3\frac{2}{3}:\frac{1}{18}+5\frac{5}{12}:\frac{7}{36}\); 4) \(13\frac{1}{2}:1\frac{1}{3}+16\frac{1}{2}\cdot1\frac{5}{11}+19\frac{1}{4}:\frac{4}{25}\).

Ответ:

  1. \[2:\frac{3}{5}+\frac{3}{5}:2+1\frac{1}{2}:6+6:1\frac{1}{2}=\frac{10}{3}+\frac{3}{10}+\frac14+4=\frac{239}{30}=7\frac{29}{30}.\]
  2. \[6\frac14\cdot8-3\frac23\cdot5\frac12+2\frac25\cdot4\frac7{12}=50-\frac{11}{3}\cdot\frac{11}{2}+\frac{12}{5}\cdot\frac{55}{12}=50-\frac{121}{6}+11=\frac{245}{6}=40\frac56.\]
  3. \[2\frac12\cdot48-3\frac23:\frac1{18}+5\frac5{12}:\frac7{36}=120-\frac{11}{3}\cdot18+\frac{65}{12}\cdot\frac{36}{7}=120-66+\frac{195}{7}=\frac{573}{7}=81\frac67.\]
  4. \[13\frac12:1\frac13+16\frac12\cdot1\frac5{11}+19\frac14:\frac4{25}=\frac{27}{2}\cdot\frac34+\frac{33}{2}\cdot\frac{16}{11}+\frac{77}{4}\cdot\frac{25}{4}=\frac{81}{8}+24+\frac{1925}{16}=\frac{2219}{16}=138\frac{11}{16}.\]
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