2.462 Выполните действия: a) 7 2/9 : 4/3 ∙ 9; б) 5 3/7 : 8/21 : 2 3/8; в) 11/21 ∙ 3/8 : 7/9; г) 5/6 : 6/11 : 1 1/11.

• а) $$7\frac{2}{9} : \frac{4}{3} \cdot 9 = \frac{65}{9} : \frac{4}{3} \cdot 9 = \frac{65}{9} \cdot \frac{3}{4} \cdot 9 = \frac{65 \cdot 3 \cdot 9}{9 \cdot 4} = \frac{65 \cdot 3}{4} = \frac{195}{4} = 48\frac{3}{4}$$
• б) $$5\frac{3}{7} : \frac{8}{21} : 2\frac{3}{8} = \frac{38}{7} : \frac{8}{21} : \frac{19}{8} = \frac{38}{7} \cdot \frac{21}{8} : \frac{19}{8} = \frac{38 \cdot 21}{7 \cdot 8} \cdot \frac{8}{19} = \frac{38 \cdot 21 \cdot 8}{7 \cdot 8 \cdot 19} = \frac{2 \cdot 3 \cdot 1}{1 \cdot 1 \cdot 1} = 6$$
• в) $$\frac{11}{21} \cdot \frac{3}{8} : \frac{7}{9} = \frac{11}{21} \cdot \frac{3}{8} \cdot \frac{9}{7} = \frac{11 \cdot 3 \cdot 9}{21 \cdot 8 \cdot 7} = \frac{11 \cdot 1 \cdot 3}{7 \cdot 8 \cdot 7} = \frac{33}{392}$$
• г) $$\frac{5}{6} : \frac{6}{11} : 1\frac{1}{11} = \frac{5}{6} : \frac{6}{11} : \frac{12}{11} = \frac{5}{6} \cdot \frac{11}{6} : \frac{12}{11} = \frac{5 \cdot 11}{6 \cdot 6} \cdot \frac{11}{12} = \frac{5 \cdot 11 \cdot 11}{6 \cdot 6 \cdot 12} = \frac{605}{432} = 1\frac{173}{432}$$

Ответ: а) $$48\frac{3}{4}$$; б) 6; в) $$\frac{33}{392}$$; г) $$1\frac{173}{432}$$