5 Вычислите значение дробного выражения: а) \(\frac{\frac{3}{7} \cdot 1,1 \cdot 1 \frac{1}{6} : 0,05}{\frac{1}{7} : 0,25 \cdot 2 \frac{2}{5}};\) б) \(\frac{0,3 \cdot 7,4 : 0,37 - 1 \frac{11}{14} \cdot 0,7}{1 + 2 \frac{1}{8} \cdot 0,16 : 0,01};\) в) \(\frac{18,55 \cdot \frac{4}{35} \cdot 4,2}{3 \frac{1}{2} \cdot 2,12 : 70};\) г) \(\frac{(2,75 \cdot \frac{3}{5} + 2,2 : 1) \cdot 1 \frac{1}{11}}{(\frac{39}{40} - 0,575) : \frac{4}{5} \cdot 0,8}.\)

Решение:

а) \(\frac{\frac{3}{7} \cdot 1,1 \cdot 1 \frac{1}{6} : 0,05}{\frac{1}{7} : 0,25 \cdot 2 \frac{2}{5}} = \frac{\frac{3}{7} \cdot \frac{11}{10} \cdot \frac{7}{6} : \frac{5}{100}}{\frac{1}{7} : \frac{25}{100} \cdot \frac{12}{5}} = \frac{\frac{3 \cdot 11 \cdot 7}{7 \cdot 10 \cdot 6} : \frac{5}{100}}{\frac{1}{7} : \frac{25 \cdot 12}{100 \cdot 5}} = \frac{\frac{11}{20} : \frac{1}{20}}{\frac{1}{7} : \frac{3}{5}} = \frac{\frac{11}{20} \cdot 20}{\frac{1}{7} \cdot \frac{5}{3}} = \frac{11}{\frac{5}{21}} = \frac{11 \cdot 21}{5} = \frac{231}{5} = 46 \frac{1}{5}\)

б) \(\frac{0,3 \cdot 7,4 : 0,37 - 1 \frac{11}{14} \cdot 0,7}{1 + 2 \frac{1}{8} \cdot 0,16 : 0,01} = \frac{0,3 \cdot 7,4 : 0,37 - \frac{25}{14} \cdot \frac{7}{10}}{1 + \frac{17}{8} \cdot \frac{16}{100} : \frac{1}{100}} = \frac{\frac{3}{10} \cdot \frac{74}{10} : \frac{37}{100} - \frac{25 \cdot 7}{14 \cdot 10}}{1 + \frac{17}{8} \cdot \frac{4}{25} \cdot 100} = \frac{\frac{3 \cdot 74 \cdot 100}{10 \cdot 10 \cdot 37} - \frac{5}{4}}{1 + \frac{17 \cdot 4 \cdot 100}{8 \cdot 25}} = \frac{\frac{3 \cdot 2 \cdot 10}{1} - \frac{5}{4}}{1 + \frac{17 \cdot 1 \cdot 10}{2 \cdot 1}} = \frac{6 - \frac{5}{4}}{1 + 34} = \frac{\frac{24 - 5}{4}}{35} = \frac{\frac{19}{4}}{35} = \frac{19}{4 \cdot 35} = \frac{19}{140}\)

в) \(\frac{18,55 \cdot \frac{4}{35} \cdot 4,2}{3 \frac{1}{2} \cdot 2,12 : 70} = \frac{\frac{1855}{100} \cdot \frac{4}{35} \cdot \frac{42}{10}}{\frac{7}{2} \cdot \frac{212}{100} : 70} = \frac{\frac{1855 \cdot 4 \cdot 42}{100 \cdot 35 \cdot 10}}{\frac{7 \cdot 212}{2 \cdot 100} : 70} = \frac{\frac{311460}{35000}}{\frac{1484}{200} : 70} = \frac{\frac{15573}{1750}}{\frac{371}{50} \cdot \frac{1}{70}} = \frac{15573 \cdot 50 \cdot 70}{1750 \cdot 371} = \frac{54505500}{649250} = 84 \)

г) \(\frac{(2,75 \cdot \frac{3}{5} + 2,2 : 1) \cdot 1 \frac{1}{11}}{(\frac{39}{40} - 0,575) : \frac{4}{5} \cdot 0,8} = \frac{(\frac{275}{100} \cdot \frac{3}{5} + \frac{22}{10} : 1) \cdot \frac{12}{11}}{(\frac{39}{40} - \frac{575}{1000}) : \frac{4}{5} \cdot \frac{8}{10}} = \frac{(\frac{11}{4} \cdot \frac{3}{5} + \frac{11}{5}) \cdot \frac{12}{11}}{(\frac{39}{40} - \frac{23}{40}) : \frac{4}{5} \cdot \frac{4}{5}} = \frac{(\frac{33}{20} + \frac{44}{20}) \cdot \frac{12}{11}}{\frac{16}{40} : \frac{16}{25}} = \frac{\frac{77}{20} \cdot \frac{12}{11}}{\frac{2}{5} \cdot \frac{25}{16}} = \frac{\frac{7 \cdot 3}{5}}{\frac{5}{8}} = \frac{21}{5} \cdot \frac{8}{5} = \frac{168}{25} = 6 \frac{18}{25}\)

Ответ: а) \(46 \frac{1}{5}\); б) \(\frac{19}{140}\); в) 84; г) \(6 \frac{18}{25}\)