407. (0,71-\frac{1}{4}): (0,71+\frac{1}{4})\cdot \frac{(-15 + 9\frac{1}{3}): 2\frac{5}{9}}{-(-19\frac{2}{3} + 11\frac{7}{9})\cdot \frac{9}{71}}

Решим по действиям:

1) \(0,71 - \frac{1}{4} = \frac{71}{100} - \frac{1}{4} = \frac{71}{100} - \frac{25}{100} = \frac{46}{100} = \frac{23}{50}\)

2) \(0,71 + \frac{1}{4} = \frac{71}{100} + \frac{1}{4} = \frac{71}{100} + \frac{25}{100} = \frac{96}{100} = \frac{24}{25}\)

3) \(\frac{23}{50} : \frac{24}{25} = \frac{23}{50} \cdot \frac{25}{24} = \frac{23}{2} \cdot \frac{1}{24} = \frac{23}{48}\)

4) \(-15 + 9\frac{1}{3} = -15 + \frac{28}{3} = -\frac{45}{3} + \frac{28}{3} = -\frac{17}{3}\)

5) \(2\frac{5}{9} = \frac{23}{9}\)

6) \(-\frac{17}{3} : \frac{23}{9} = -\frac{17}{3} \cdot \frac{9}{23} = -\frac{17}{1} \cdot \frac{3}{23} = -\frac{51}{23}\)

7) \(-19\frac{2}{3} + 11\frac{7}{9} = -\frac{59}{3} + \frac{106}{9} = -\frac{177}{9} + \frac{106}{9} = -\frac{71}{9}\)

8) \(-\frac{71}{9} \cdot \frac{9}{71} = -\frac{1}{1} \cdot \frac{1}{1} = -1\)

9) \(\frac{-\frac{51}{23}}{-(-1)} = \frac{-\frac{51}{23}}{1} = -\frac{51}{23}\)

10) \(\frac{23}{48} \cdot \left(-\frac{51}{23}\right) = \frac{1}{48} \cdot ( -51) = -\frac{51}{48} = -\frac{17}{16} = -1\frac{1}{16}\)