6. Вычислите: a) 1\frac{5}{12} \cdot 1\frac{1}{3} б) 2\frac{3}{5} \cdot 1\frac{4}{11} в) 3\frac{1}{3} \cdot 1\frac{7}{23} г) 4\frac{2}{5} \cdot \frac{5}{12} д) 1\frac{5}{12} : 2\frac{2}{3} е) 11\frac{2}{5} : 3\frac{3}{4} ж) 8\frac{1}{3} : 2\frac{2}{9} з) 9\frac{5}{7} : 1\frac{23}{28} и) 6\frac{2}{3} : 1\frac{1}{11} к) 57 : \frac{19}{24} л) \frac{6}{11} : 3

6. Вычислите:

a) $$1\frac{5}{12} \cdot 1\frac{1}{3} = \frac{17}{12} \cdot \frac{4}{3} = \frac{17 \cdot 4}{12 \cdot 3} = \frac{17 \cdot 1}{3 \cdot 3} = \frac{17}{9} = 1\frac{8}{9}$$

б) $$2\frac{3}{5} \cdot 1\frac{4}{11} = \frac{13}{5} \cdot \frac{15}{11} = \frac{13 \cdot 15}{5 \cdot 11} = \frac{13 \cdot 3}{1 \cdot 11} = \frac{39}{11} = 3\frac{6}{11}$$

в) $$3\frac{1}{3} \cdot 1\frac{7}{23} = \frac{10}{3} \cdot \frac{30}{23} = \frac{10 \cdot 30}{3 \cdot 23} = \frac{10 \cdot 10}{1 \cdot 23} = \frac{100}{23} = 4\frac{8}{23}$$

г) $$4\frac{2}{5} \cdot \frac{5}{12} = \frac{22}{5} \cdot \frac{5}{12} = \frac{22 \cdot 5}{5 \cdot 12} = \frac{22 \cdot 1}{1 \cdot 12} = \frac{22}{12} = \frac{11}{6} = 1\frac{5}{6}$$

д) $$1\frac{5}{12} : 2\frac{2}{3} = \frac{17}{12} : \frac{8}{3} = \frac{17}{12} \cdot \frac{3}{8} = \frac{17 \cdot 3}{12 \cdot 8} = \frac{17 \cdot 1}{4 \cdot 8} = \frac{17}{32}$$

е) $$11\frac{2}{5} : 3\frac{3}{4} = \frac{57}{5} : \frac{15}{4} = \frac{57}{5} \cdot \frac{4}{15} = \frac{57 \cdot 4}{5 \cdot 15} = \frac{19 \cdot 4}{5 \cdot 5} = \frac{76}{25} = 3\frac{1}{25}$$

ж) $$8\frac{1}{3} : 2\frac{2}{9} = \frac{25}{3} : \frac{20}{9} = \frac{25}{3} \cdot \frac{9}{20} = \frac{25 \cdot 9}{3 \cdot 20} = \frac{5 \cdot 3}{1 \cdot 4} = \frac{15}{4} = 3\frac{3}{4}$$

з) $$9\frac{5}{7} : 1\frac{23}{28} = \frac{68}{7} : \frac{51}{28} = \frac{68}{7} \cdot \frac{28}{51} = \frac{68 \cdot 28}{7 \cdot 51} = \frac{4 \cdot 4}{1 \cdot 3} = \frac{16}{3} = 5\frac{1}{3}$$

и) $$6\frac{2}{3} : 1\frac{1}{11} = \frac{20}{3} : \frac{12}{11} = \frac{20}{3} \cdot \frac{11}{12} = \frac{20 \cdot 11}{3 \cdot 12} = \frac{5 \cdot 11}{3 \cdot 3} = \frac{55}{9} = 6\frac{1}{9}$$

к) $$57 : \frac{19}{24} = \frac{57}{1} \cdot \frac{24}{19} = \frac{57 \cdot 24}{1 \cdot 19} = \frac{3 \cdot 24}{1 \cdot 1} = 72$$

л) $$\frac{6}{11} : 3 = \frac{6}{11} : \frac{3}{1} = \frac{6}{11} \cdot \frac{1}{3} = \frac{6 \cdot 1}{11 \cdot 3} = \frac{2 \cdot 1}{11 \cdot 1} = \frac{2}{11}$$

Ответ: a) $$1\frac{8}{9}$$; б) $$3\frac{6}{11}$$; в) $$4\frac{8}{23}$$; г) $$1\frac{5}{6}$$; д) $$\frac{17}{32}$$; е) $$3\frac{1}{25}$$; ж) $$3\frac{3}{4}$$; з) $$5\frac{1}{3}$$; и) $$6\frac{1}{9}$$; к) 72; л) $$\frac{2}{11}$$