4) \(99 1/9 : 44,6 - 4 7/12 \cdot 4/11 + 13 11/18\) : 25,5

Решение:

4. Четвёртый пример:

1. \( 99\frac{1}{9} = \frac{892}{9} \)
2. \( 44,6 = 44\frac{6}{10} = 44\frac{3}{5} = \frac{223}{5} \)
3. \( \frac{892}{9} : \frac{223}{5} = \frac{892}{9} \cdot \frac{5}{223} = 4 \cdot \frac{5}{9} = \frac{20}{9} \)
4. \( 4\frac{7}{12} = \frac{55}{12} \)
5. \( \frac{55}{12} \cdot \frac{4}{11} = \frac{5}{3} \cdot \frac{1}{1} = \frac{5}{3} \)
6. \( 13\frac{11}{18} = \frac{245}{18} \)
7. \( \frac{20}{9} - \frac{5}{3} + \frac{245}{18} = \frac{40}{18} - \frac{30}{18} + \frac{245}{18} = \frac{10 + 245}{18} = \frac{255}{18} = \frac{85}{6} \)
8. \( 25,5 = 25\frac{1}{2} = \frac{51}{2} \)
9. \( \frac{85}{6} : \frac{51}{2} = \frac{85}{6} \cdot \frac{2}{51} = \frac{85}{3} \cdot \frac{1}{51} = \frac{5 \cdot 17}{3} \cdot \frac{1}{3 \cdot 17} = \frac{5}{9} \)

Ответ: 5/9