6. Вычислите: a) 1\frac{1}{4}·1\frac{1}{4} б) 2\frac{5}{11}·\frac{4}{11} в) 3\frac{5}{6}·1\frac{17}{23} г) 4\frac{1}{2}·\frac{2}{5} д) 1\frac{1}{2}:2\frac{2}{5} e) 11\frac{2}{5}:3\frac{3}{4} ж) 8\frac{1}{2}:2\frac{1}{23} з) 9\frac{1}{7}:1\frac{12}{28} и) 6\frac{5}{11}:1\frac{1}{8} к) 57:\frac{19}{24} л) 6\frac{1}{11}:3

a) $$ 1\frac{1}{4} \cdot 1\frac{1}{4} = \frac{5}{4} \cdot \frac{5}{4} = \frac{25}{16} = 1\frac{9}{16} $$

б) $$ 2\frac{5}{11} \cdot \frac{4}{11} = \frac{27}{11} \cdot \frac{4}{11} = \frac{108}{121} $$

в) $$ 3\frac{5}{6} \cdot 1\frac{17}{23} = \frac{23}{6} \cdot \frac{40}{23} = \frac{40}{6} = \frac{20}{3} = 6\frac{2}{3} $$

г) $$ 4\frac{1}{2} \cdot \frac{2}{5} = \frac{9}{2} \cdot \frac{2}{5} = \frac{9}{5} = 1\frac{4}{5} $$

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

е) $$ 11\frac{2}{5} : 3\frac{3}{4} = \frac{57}{5} : \frac{15}{4} = \frac{57}{5} \cdot \frac{4}{15} = \frac{228}{75} = \frac{76}{25} = 3\frac{1}{25} $$

ж) $$ 8\frac{1}{2} : 2\frac{1}{23} = \frac{17}{2} : \frac{47}{23} = \frac{17}{2} \cdot \frac{23}{47} = \frac{391}{94} = 4\frac{15}{94} $$

з) $$ 9\frac{1}{7} : 1\frac{12}{28} = \frac{64}{7} : \frac{40}{28} = \frac{64}{7} \cdot \frac{28}{40} = \frac{64 \cdot 4}{40} = \frac{256}{40} = \frac{32}{5} = 6\frac{2}{5} $$

и) $$ 6\frac{5}{11} : 1\frac{1}{8} = \frac{71}{11} : \frac{9}{8} = \frac{71}{11} \cdot \frac{8}{9} = \frac{568}{99} = 5\frac{73}{99} $$

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

л) $$ 6\frac{1}{11} : 3 = \frac{67}{11} : 3 = \frac{67}{11} \cdot \frac{1}{3} = \frac{67}{33} = 2\frac{1}{33} $$

Ответ: a) 1 9/16; б) 108/121; в) 6 2/3; г) 1 4/5; д) 5/8; е) 3 1/25; ж) 4 15/94; з) 6 2/5; и) 5 73/99; к) 72; л) 2 1/33.