Выполните действия: 1)90⋅4/63; 2)15/34⋅16; 3)11/26⋅1/2; 4)1/3⋅1/5; 8)5⋅5/66⋅9/20; 6)2/55⋅35/4; 7)2⋅14/15⋅5/16; 8)8⋅3/4⋅11/15; 9)12:10/11; 10)2/7:16; 11)9/32:3/4; 12)3:4;

Решение:

1) \(90 \cdot \frac{4}{63} = \frac{90 \cdot 4}{63} = \frac{360}{63} = \frac{40}{7} = 5\frac{5}{7}\) 2) \(\frac{15}{34} \cdot 16 = \frac{15 \cdot 16}{34} = \frac{15 \cdot 8}{17} = \frac{120}{17} = 7\frac{1}{17}\) 3) \(\frac{11}{26} \cdot \frac{1}{2} = \frac{11 \cdot 1}{26 \cdot 2} = \frac{11}{52}\) 4) \(\frac{1}{3} \cdot \frac{1}{5} = \frac{1 \cdot 1}{3 \cdot 5} = \frac{1}{15}\) 5) \(5\frac{5}{66} \cdot \frac{9}{20} = \frac{5 \cdot 66 + 5}{66} \cdot \frac{9}{20} = \frac{335}{66} \cdot \frac{9}{20} = \frac{335 \cdot 9}{66 \cdot 20} = \frac{335 \cdot 3}{22 \cdot 20} = \frac{1005}{440} = \frac{201}{88} = 2\frac{25}{88}\) 6) \(\frac{2}{55} \cdot \frac{35}{4} = \frac{2 \cdot 35}{55 \cdot 4} = \frac{1 \cdot 7}{11 \cdot 2} = \frac{7}{22}\) 7) \(2\frac{14}{15} \cdot 5\frac{7}{16} = \frac{2 \cdot 15 + 14}{15} \cdot \frac{5 \cdot 16 + 7}{16} = \frac{44}{15} \cdot \frac{87}{16} = \frac{11}{5} \cdot \frac{87}{4} = \frac{11 \cdot 87}{5 \cdot 4} = \frac{957}{20} = 47\frac{17}{20}\) 8) \(8\frac{3}{4} \cdot 1\frac{11}{15} = \frac{8 \cdot 4 + 3}{4} \cdot \frac{1 \cdot 15 + 11}{15} = \frac{35}{4} \cdot \frac{26}{15} = \frac{7}{2} \cdot \frac{13}{3} = \frac{7 \cdot 13}{2 \cdot 3} = \frac{91}{6} = 15\frac{1}{6}\) 9) \(12 : \frac{10}{11} = 12 \cdot \frac{11}{10} = \frac{12 \cdot 11}{10} = \frac{6 \cdot 11}{5} = \frac{66}{5} = 13\frac{1}{5}\) 10) \(\frac{2}{7} : 16 = \frac{2}{7} \cdot \frac{1}{16} = \frac{2}{7 \cdot 16} = \frac{1}{7 \cdot 8} = \frac{1}{56}\) 11) \(\frac{9}{32} : \frac{3}{4} = \frac{9}{32} \cdot \frac{4}{3} = \frac{9 \cdot 4}{32 \cdot 3} = \frac{3 \cdot 1}{8 \cdot 1} = \frac{3}{8}\) 12) \(3\frac{1}{4} : 4\frac{1}{3} = \frac{3 \cdot 4 + 1}{4} : \frac{4 \cdot 3 + 1}{3} = \frac{13}{4} : \frac{13}{3} = \frac{13}{4} \cdot \frac{3}{13} = \frac{13 \cdot 3}{4 \cdot 13} = \frac{3}{4}\)

Ответ: 1) \(5\frac{5}{7}\); 2) \(7\frac{1}{17}\); 3) \(\frac{11}{52}\); 4) \(\frac{1}{15}\); 5) \(2\frac{25}{88}\); 6) \(\frac{7}{22}\); 7) \(47\frac{17}{20}\); 8) \(15\frac{1}{6}\); 9) \(13\frac{1}{5}\); 10) \(\frac{1}{56}\); 11) \(\frac{3}{8}\); 12) \(\frac{3}{4}\)

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