Решите пример: $$2 \frac{1}{4} \cdot 8 - 3 \frac{2}{3} \cdot 5 \frac{1}{2} + 2 \frac{2}{3} \cdot 9 \frac{1}{12}$$.

Решим пример по действиям:

1. $$2 \frac{1}{4} \cdot 8 = \frac{9}{4} \cdot 8 = \frac{9 \cdot 8}{4} = \frac{9 \cdot 2}{1} = 18$$
2. $$3 \frac{2}{3} \cdot 5 \frac{1}{2} = \frac{11}{3} \cdot \frac{11}{2} = \frac{11 \cdot 11}{3 \cdot 2} = \frac{121}{6} = 20 \frac{1}{6}$$
3. $$2 \frac{2}{3} \cdot 9 \frac{1}{12} = \frac{8}{3} \cdot \frac{109}{12} = \frac{2 \cdot 109}{3 \cdot 3} = \frac{218}{9} = 24 \frac{2}{9}$$
4. $$18 - 20 \frac{1}{6} = 17 \frac{6}{6} - 20 \frac{1}{6} = -3 \frac{5}{6}$$
5. $$-3 \frac{5}{6} + 24 \frac{2}{9} = -3 \frac{15}{18} + 24 \frac{4}{18} = 20 \frac{18}{18} + \frac{4}{18} - \frac{15}{18} = 20 \frac{7}{18}$$

Ответ: $$20 \frac{7}{18}$$.