2.462 Выполните действия: 1 a) 7:4-9; 6) 5:3-8 23; в) 1:38:1; 9 3 21 8 21 9 7 6 11 1 г) 6 11 :11 к) 4:1 36

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

б) $$5\frac{3}{7} : \frac{8}{21} : 23\frac{5}{8} = \frac{38}{7} : \frac{8}{21} : \frac{189}{8} = \frac{38}{7} \cdot \frac{21}{8} \cdot \frac{8}{189} = \frac{38 \cdot 21 \cdot 8}{7 \cdot 8 \cdot 189} = \frac{38 \cdot 3}{189} = \frac{38 \cdot 3}{63 \cdot 3} = \frac{38}{63}$$

в) $$1\frac{11}{21} \cdot 3\frac{8}{9} : 1\frac{1}{7} = \frac{32}{21} \cdot \frac{35}{9} : \frac{8}{7} = \frac{32}{21} \cdot \frac{35}{9} \cdot \frac{7}{8} = \frac{32 \cdot 35 \cdot 7}{21 \cdot 9 \cdot 8} = \frac{4 \cdot 8 \cdot 5 \cdot 7 \cdot 7}{3 \cdot 7 \cdot 9 \cdot 8} = \frac{4 \cdot 5 \cdot 7}{3 \cdot 9} = \frac{140}{27} = 5\frac{5}{27}$$

г) $$6\frac{5}{6} : 1\frac{1}{11} : 1\frac{1}{11} = \frac{41}{6} : \frac{12}{11} : \frac{12}{11} = \frac{41}{6} \cdot \frac{11}{12} \cdot \frac{11}{12} = \frac{41 \cdot 11 \cdot 11}{6 \cdot 12 \cdot 12} = \frac{4961}{864} = 5\frac{641}{864}$$

к) $$4 : 1\frac{1}{36} = 4 : \frac{37}{36} = 4 \cdot \frac{36}{37} = \frac{4 \cdot 36}{37} = \frac{144}{37} = 3\frac{33}{37}$$

Ответ: a) $$15$$, б) $$\frac{38}{63}$$, в) $$5\frac{5}{27}$$, г) $$5\frac{641}{864}$$, к) $$3\frac{33}{37}$$