4.61 Выполните действия: а) \(\frac{\frac{2,8}{5,7} \cdot \frac{3}{4} - \frac{2,3}{5,1} : 2 \frac{12}{17}}{11,07 : 4,1 + 0,7 \cdot 24}\) б) \(\frac{(13,23 + 6,77) \cdot 0,02}{18: 11,25}\) +

Решим пример 4.61

a) \(\frac{\frac{2,8}{5,7} \cdot \frac{3}{4} - \frac{2,3}{5,1} : 2 \frac{12}{17}}{11,07 : 4,1 + 0,7 \cdot 24}\)

1. \(\frac{2,8}{5,7} \cdot \frac{3}{4} = \frac{28}{57} \cdot \frac{3}{4} = \frac{7 \cdot 3}{57} = \frac{21}{57} = \frac{7}{19}\)
2. \(2 \frac{12}{17} = \frac{2 \cdot 17 + 12}{17} = \frac{34 + 12}{17} = \frac{46}{17}\)
3. \(\frac{2,3}{5,1} : \frac{46}{17} = \frac{23}{51} : \frac{46}{17} = \frac{23}{51} \cdot \frac{17}{46} = \frac{1}{3} \cdot \frac{1}{2} = \frac{1}{6}\)
4. \(\frac{7}{19} - \frac{1}{6} = \frac{7 \cdot 6 - 1 \cdot 19}{19 \cdot 6} = \frac{42 - 19}{114} = \frac{23}{114}\)
5. \(11,07 : 4,1 = 110,7 : 41 = 2,7\)
6. \(0,7 \cdot 24 = 16,8\)
7. \(2,7 + 16,8 = 19,5\)
8. \(\frac{23}{114} : 19,5 = \frac{23}{114} : \frac{195}{10} = \frac{23}{114} \cdot \frac{10}{195} = \frac{23}{57 \cdot 2} \cdot \frac{2 \cdot 5}{39 \cdot 5} = \frac{23}{57} \cdot \frac{1}{39} = \frac{23}{2223}\)

Ответ: \(\frac{23}{2223}\)

б) \(\frac{(13,23 + 6,77) \cdot 0,02}{18: 11,25}\) +

1. \(13,23 + 6,77 = 20\)
2. \(20 \cdot 0,02 = 0,4\)
3. \(18 : 11,25 = 1800 : 1125 = 360 : 225 = 72 : 45 = 8 : 5 = \frac{8}{5} = 1,6\)
4. \(0,4 : 1,6 = 4 : 16 = 1 : 4 = 0,25\)

Ответ: 0,25