5) (50,2 : 41 5/6 - 18,04 : 50 1/9) \(\cdot\) 0,05 + 4,2

Решение:

5. Пятый пример:

1. \( 50,2 = 50\frac{2}{10} = 50\frac{1}{5} = \frac{251}{5} \)
2. \( 41\frac{5}{6} = \frac{251}{6} \)
3. \( \frac{251}{5} : \frac{251}{6} = \frac{251}{5} \cdot \frac{6}{251} = \frac{6}{5} \)
4. \( 18,04 = 18\frac{4}{100} = 18\frac{1}{25} = \frac{451}{25} \)
5. \( 50\frac{1}{9} = \frac{451}{9} \)
6. \( \frac{451}{25} : \frac{451}{9} = \frac{451}{25} \cdot \frac{9}{451} = \frac{9}{25} \)
7. \( \frac{6}{5} - \frac{9}{25} = \frac{30-9}{25} = \frac{21}{25} \)
8. \( \frac{21}{25} \cdot 0,05 = \frac{21}{25} \cdot \frac{5}{100} = \frac{21}{5} \cdot \frac{1}{100} = \frac{21}{500} \)
9. \( \frac{21}{500} + 4,2 = \frac{21}{500} + \frac{42}{10} = \frac{21}{500} + \frac{21}{5} = \frac{21 + 2100}{500} = \frac{2121}{500} = 4,242 \)

Ответ: 4,242