2) Вычислите: 1) $$\frac{18}{25} : \frac{3}{5}$$; 2) $$2\frac{5}{8} : 2\frac{1}{4}$$; 3) $$7 : \frac{14}{15}$$; 4) $$\frac{16}{17} : 8.$$

Решение:

1. $$\frac{18}{25} : \frac{3}{5} = \frac{18}{25} \cdot \frac{5}{3} = \frac{18 \cdot 5}{25 \cdot 3} = \frac{6 \cdot 3 \cdot 5}{5 \cdot 5 \cdot 3} = \frac{6}{5} = 1\frac{1}{5}$$
2. $$2\frac{5}{8} : 2\frac{1}{4} = \frac{21}{8} : \frac{9}{4} = \frac{21}{8} \cdot \frac{4}{9} = \frac{21 \cdot 4}{8 \cdot 9} = \frac{3 \cdot 7 \cdot 4}{2 \cdot 4 \cdot 3 \cdot 3} = \frac{7}{2 \cdot 3} = \frac{7}{6} = 1\frac{1}{6}$$
3. $$7 : \frac{14}{15} = 7 \cdot \frac{15}{14} = \frac{7 \cdot 15}{14} = \frac{7 \cdot 15}{2 \cdot 7} = \frac{15}{2} = 7\frac{1}{2}$$
4. $$\frac{16}{17} : 8 = \frac{16}{17} \cdot \frac{1}{8} = \frac{16 \cdot 1}{17 \cdot 8} = \frac{2 \cdot 8}{17 \cdot 8} = \frac{2}{17}$$

Ответ: 1) $$1\frac{1}{5}$$; 2) $$1\frac{1}{6}$$; 3) $$7\frac{1}{2}$$; 4) $$\frac{2}{17}$$.