2.537/ Вычислите: 1) $$1\frac{1}{4}:2\frac{1}{4} \cdot 1\frac{2}{7}$$; 2) $$4\frac{1}{3} \cdot 1\frac{7}{8}:1\frac{13}{15}$$; 3) $$1\frac{3}{7}:1\frac{11}{15}:4\frac{5}{7}$$; 4) $$1\frac{6}{7}:3\frac{5}{7} \cdot \frac{5}{9}$$

Решение:

1) $$1\frac{1}{4}:2\frac{1}{4} \cdot 1\frac{2}{7} = \frac{5}{4} : \frac{9}{4} \cdot \frac{9}{7} = \frac{5}{4} \cdot \frac{4}{9} \cdot \frac{9}{7} = \frac{5 \cdot 1 \cdot 1}{1 \cdot 1 \cdot 7} = \frac{5}{7}$$

2) $$4\frac{1}{3} \cdot 1\frac{7}{8}:1\frac{13}{15} = \frac{13}{3} \cdot \frac{15}{8} : \frac{28}{15} = \frac{13}{3} \cdot \frac{15}{8} \cdot \frac{15}{28} = \frac{13 \cdot 5 \cdot 5}{8 \cdot 28} = \frac{325}{224} = 1\frac{101}{224}$$

3) $$1\frac{3}{7}:1\frac{11}{15}:4\frac{5}{7} = \frac{10}{7} : \frac{26}{15} : \frac{33}{7} = \frac{10}{7} \cdot \frac{15}{26} \cdot \frac{7}{33} = \frac{10 \cdot 15 \cdot 1}{1 \cdot 26 \cdot 33} = \frac{150}{858} = \frac{25}{143}$$

4) $$1\frac{6}{7}:3\frac{5}{7} \cdot \frac{5}{9} = \frac{13}{7} : \frac{26}{7} \cdot \frac{5}{9} = \frac{13}{7} \cdot \frac{7}{26} \cdot \frac{5}{9} = \frac{13 \cdot 1 \cdot 5}{1 \cdot 26 \cdot 9} = \frac{65}{234} = \frac{5}{18}$$

Ответ: 1) $$\frac{5}{7}$$; 2) $$1\frac{101}{224}$$; 3) $$\frac{25}{143}$$; 4) $$\frac{5}{18}$$