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

Выполним действия с дробями.

а) $$7 \frac{2}{9} : 4 \frac{1}{3} \cdot 9 = \frac{65}{9} : \frac{13}{3} \cdot 9 = \frac{65}{9} \cdot \frac{3}{13} \cdot 9 = \frac{65 \cdot 3 \cdot 9}{9 \cdot 13} = \frac{65 \cdot 3}{13} = 5 \cdot 3 = 15$$

б) $$5 \frac{3}{7} : \frac{8}{21} : 2 \frac{3}{8} = \frac{38}{7} : \frac{8}{21} : \frac{19}{8} = \frac{38}{7} \cdot \frac{21}{8} : \frac{19}{8} = \frac{38 \cdot 21}{7 \cdot 8} \cdot \frac{8}{19} = \frac{38 \cdot 21 \cdot 8}{7 \cdot 8 \cdot 19} = \frac{2 \cdot 3}{1} = 6$$

в) $$1 \frac{11}{21} \cdot 3 \frac{8}{9} : 1 \frac{7}{9} = \frac{32}{21} \cdot \frac{35}{9} : \frac{16}{9} = \frac{32}{21} \cdot \frac{35}{9} \cdot \frac{9}{16} = \frac{32 \cdot 35 \cdot 9}{21 \cdot 9 \cdot 16} = \frac{2 \cdot 5}{3} = \frac{10}{3} = 3 \frac{1}{3}$$

г) $$\frac{5}{6} : \frac{11}{11} : 1 \frac{1}{11} = \frac{5}{6} : 1 : \frac{12}{11} = \frac{5}{6} \cdot \frac{1}{1} \cdot \frac{11}{12} = \frac{5 \cdot 11}{6 \cdot 12} = \frac{55}{72}$$

Ответ: а) 15, б) 6, в) $$3 \frac{1}{3}$$, г) $$\frac{55}{72}$$.