4 \(\frac{2}{15}\) : 11 + 7 : 2 \(\frac{1}{3}\) - 1 \(\frac{2}{3}\) \(\cdot\) 3 \(\frac{1}{12}\) 20 : \(3 \frac{1}{4} - 2 \frac{1}{4}\) \(\cdot\) 4 \(\frac{2}{3}\) + 15 : 3 \(\frac{3}{8}\) \(\cdot\) \(\frac{1}{18}\)

Решение:

Первое выражение:

1. \( 4 \frac{2}{15} = \frac{4 \times 15 + 2}{15} = \frac{62}{15} \)
2. \( 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3} \)
3. \( 1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3} \)
4. \( 3 \frac{1}{12} = \frac{3 \times 12 + 1}{12} = \frac{37}{12} \)
5. \( \frac{62}{15} : 11 = \frac{62}{15 \times 11} = \frac{62}{165} \)
6. \( 7 : \frac{7}{3} = 7 \times \frac{3}{7} = 3 \)
7. \( \frac{5}{3} \cdot \frac{37}{12} = \frac{5 \times 37}{3 \times 12} = \frac{185}{36} \)
8. \( \frac{62}{165} + 3 - \frac{185}{36} \)
9. \( \frac{62}{165} + \frac{3 \times 165}{165} - \frac{185}{36} = \frac{62 + 495}{165} - \frac{185}{36} = \frac{557}{165} - \frac{185}{36} \)
10. \( \frac{557 \times 12}{1980} - \frac{185 \times 55}{1980} = \frac{6684 - 10175}{1980} = \frac{-3491}{1980} \)

Второе выражение:

1. \( 3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4} \)
2. \( 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4} \)
3. \( 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{14}{3} \)
4. \( 3 \frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{27}{8} \)
5. \( \frac{13}{4} - \frac{9}{4} = \frac{13-9}{4} = \frac{4}{4} = 1 \)
6. \( 20 : 1 = 20 \)
7. \( 20 \cdot \frac{14}{3} = \frac{20 \times 14}{3} = \frac{280}{3} \)
8. \( 15 : \frac{27}{8} = 15 \times \frac{8}{27} = \frac{15 \times 8}{27} = \frac{5 \times 8}{9} = \frac{40}{9} \)
9. \( \frac{40}{9} \cdot \frac{1}{18} = \frac{40}{9 \times 18} = \frac{40}{162} = \frac{20}{81} \)
10. \( \frac{280}{3} + \frac{20}{81} \)
11. \( \frac{280 \times 27}{81} + \frac{20}{81} = \frac{7560 + 20}{81} = \frac{7580}{81} \)

Ответ: \( -\frac{3491}{1980} \) ; \( \frac{7580}{81} \)