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

a) $$7\frac{2}{9} : \frac{4}{3} \cdot 9 = \frac{65}{9} : \frac{4}{3} \cdot 9 = \frac{65}{9} \cdot \frac{3}{4} \cdot 9 = \frac{65 \cdot 3 \cdot 9}{9 \cdot 4} = \frac{65 \cdot 3}{4} = \frac{195}{4} = 48\frac{3}{4}$$ Ответ: $$48\frac{3}{4}$$ б) $$5\frac{3}{7} : \frac{21}{8} \cdot 2\frac{2}{3} = \frac{38}{7} : \frac{21}{8} \cdot \frac{8}{3} = \frac{38}{7} \cdot \frac{8}{21} \cdot \frac{8}{3} = \frac{38 \cdot 8 \cdot 8}{7 \cdot 21 \cdot 3} = \frac{2432}{441} = 5 \frac{227}{441}$$ Ответ: $$5 \frac{227}{441}$$ в) $$1\frac{11}{21} \cdot \frac{8}{9} : 1\frac{1}{9} = \frac{32}{21} \cdot \frac{8}{9} : \frac{10}{9} = \frac{32}{21} \cdot \frac{8}{9} \cdot \frac{9}{10} = \frac{32 \cdot 8 \cdot 9}{21 \cdot 9 \cdot 10} = \frac{32 \cdot 8}{21 \cdot 10} = \frac{256}{210} = \frac{128}{105} = 1 \frac{23}{105}$$ Ответ: $$1 \frac{23}{105}$$ г) $$\frac{5}{6} : \frac{11}{6} \cdot 1\frac{1}{11} = \frac{5}{6} : \frac{11}{6} \cdot \frac{12}{11} = \frac{5}{6} \cdot \frac{6}{11} \cdot \frac{12}{11} = \frac{5 \cdot 6 \cdot 12}{6 \cdot 11 \cdot 11} = \frac{5 \cdot 12}{11 \cdot 11} = \frac{60}{121}$$ Ответ: $$\frac{60}{121}$$