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

a) Выполним действия:

1) Переведем смешанную дробь в неправильную: \(4 \frac{3}{4} = \frac{4 \cdot 4 + 3}{4} = \frac{19}{4}\); \(2 \frac{12}{17} = \frac{2 \cdot 17 + 12}{17} = \frac{46}{17}\).

2) \(\frac{2,8 \cdot 4 \frac{3}{4}}{5,7}\) = \(\frac{2,8 \cdot \frac{19}{4}}{5,7}\) = \(\frac{2,8 \cdot 19}{4 \cdot 5,7}\) = \(\frac{2,8 \cdot 19}{4 \cdot 5,7}\) = \(\frac{28 \cdot 19}{4 \cdot 57}\) = \(\frac{7 \cdot 19}{57}\) = \(\frac{7 \cdot 19}{3 \cdot 19}\) = \(\frac{7}{3}\).

3) \(\frac{2,3}{5,1}\) : 2 \(\frac{12}{17}\) = \(\frac{2,3}{5,1}\) : \(\frac{46}{17}\) = \(\frac{2,3}{5,1}\) \(\cdot \frac{17}{46}\) = \(\frac{23}{51}\) \(\cdot \frac{17}{46}\) = \(\frac{1}{3}\) \(\cdot \frac{1}{2}\) = \(\frac{1}{6}\).

4) \(\frac{7}{3}\) : \(\frac{1}{6}\) = \(\frac{7}{3}\) \(\cdot \frac{6}{1}\) = 7 \(\cdot\) 2 = 14.

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) 14 : 19,5 = \(\frac{14}{19,5}\) = \(\frac{140}{195}\) = \(\frac{28}{39}\).

Ответ: \(\frac{28}{39}\)