Вычислите: (11\frac{1}{3} \cdot 3; 1\frac{2}{5} \cdot 2; (\frac{3}{4})^2; (1\frac{1}{3})^3; \frac{2}{5} \cdot (\frac{1}{2} + \frac{5}{6}); \frac{7}{8} : 28; 15 : 1\frac{1}{2}; 20 : 16; \frac{3}{5} - \frac{1}{3} \cdot \frac{5}{6})

Решение: 1. (11\frac{1}{3} \cdot 3 = \frac{34}{3} \cdot 3 = 34) 2. (1\frac{2}{5} \cdot 2 = \frac{7}{5} \cdot 2 = \frac{14}{5} = 2\frac{4}{5}) 3. ((\frac{3}{4})^2 = \frac{3}{4} \cdot \frac{3}{4} = \frac{9}{16}) 4. ((1\frac{1}{3})^3 = (\frac{4}{3})^3 = \frac{4}{3} \cdot \frac{4}{3} \cdot \frac{4}{3} = \frac{64}{27} = 2\frac{10}{27}) 5. \[\begin{aligned} \frac{2}{5} \cdot (\frac{1}{2} + \frac{5}{6}) &= \frac{2}{5} \cdot (\frac{3}{6} + \frac{5}{6}) \\ &= \frac{2}{5} \cdot \frac{8}{6} = \frac{2}{5} \cdot \frac{4}{3} = \frac{8}{15} \end{aligned}\] 6. \[\begin{aligned} \frac{7}{8} : 28 &= \frac{7}{8} : \frac{28}{1} \\ &= \frac{7}{8} \cdot \frac{1}{28} = \frac{7}{8 \cdot 28} = \frac{1}{8 \cdot 4} = \frac{1}{32} \end{aligned}\] 7. \[\begin{aligned} 15 : 1\frac{1}{2} &= 15 : \frac{3}{2} \\ &= \frac{15}{1} \cdot \frac{2}{3} = \frac{15 \cdot 2}{3} = \frac{30}{3} = 10 \end{aligned}\] 8. (20 : 16 = \frac{20}{16} = \frac{5}{4} = 1\frac{1}{4}) 9. \[\begin{aligned} \frac{3}{5} - \frac{1}{3} \cdot \frac{5}{6} &= \frac{3}{5} - \frac{5}{18} \\ &= \frac{3 \cdot 18 - 5 \cdot 5}{5 \cdot 18} = \frac{54 - 25}{90} = \frac{29}{90} \end{aligned}\]