19\(\frac{1}{2}\)\(\cdot\)\(\left\)\(3\frac{1}{2}-1\frac{11}{20}\right\)-\(\frac{111}{200}\):\(\frac{3}{20}\)

Решение:

1. \( 3\frac{1}{2} = \frac{7}{2} \)
2. \( 1\frac{11}{20} = \frac{31}{20} \)
3. \( \frac{7}{2} - \frac{31}{20} = \frac{70}{20} - \frac{31}{20} = \frac{39}{20} \)
4. \( 19\frac{1}{2} = \frac{39}{2} \)
5. \( \frac{39}{2} \cdot \frac{39}{20} = \frac{1521}{40} \)
6. \( \frac{111}{200} : \frac{3}{20} = \frac{111}{200} \cdot \frac{20}{3} = \frac{111}{10} \cdot \frac{1}{3} = \frac{37}{10} \)
7. \( \frac{1521}{40} - \frac{37}{10} = \frac{1521}{40} - \frac{148}{40} = \frac{1373}{40} \)

Ответ: \(\frac{1373}{40}\)