1. Выполните действие: a) 5 \frac{7}{9} \cdot \frac{9}{8}; б) \frac{4}{27} \cdot \frac{9}{16}; в) 5 \frac{5}{6} \cdot 2 \frac{4}{7}; г) 1 \frac{5}{12} \cdot 24; д) \frac{4}{9} : \frac{16}{45}; e) \frac{18}{19} : 6.

Ответ:

а) 5 \frac{7}{9} \cdot \frac{9}{8} = \frac{5 \cdot 9 + 7}{9} \cdot \frac{9}{8} = \frac{45+7}{9} \cdot \frac{9}{8} = \frac{52}{9} \cdot \frac{9}{8} = \frac{52 \cdot 9}{9 \cdot 8} = \frac{52}{8} = \frac{13}{2} = 6 \frac{1}{2}

б) \frac{4}{27} \cdot \frac{9}{16} = \frac{4 \cdot 9}{27 \cdot 16} = \frac{1 \cdot 1}{3 \cdot 4} = \frac{1}{12}

в) 5 \frac{5}{6} \cdot 2 \frac{4}{7} = \frac{5 \cdot 6 + 5}{6} \cdot \frac{2 \cdot 7 + 4}{7} = \frac{30+5}{6} \cdot \frac{14+4}{7} = \frac{35}{6} \cdot \frac{18}{7} = \frac{35 \cdot 18}{6 \cdot 7} = \frac{5 \cdot 3}{1 \cdot 1} = 15

г) 1 \frac{5}{12} \cdot 24 = \frac{1 \cdot 12 + 5}{12} \cdot 24 = \frac{12+5}{12} \cdot 24 = \frac{17}{12} \cdot 24 = \frac{17 \cdot 24}{12} = 17 \cdot 2 = 34

д) \frac{4}{9} : \frac{16}{45} = \frac{4}{9} \cdot \frac{45}{16} = \frac{4 \cdot 45}{9 \cdot 16} = \frac{1 \cdot 5}{1 \cdot 4} = \frac{5}{4} = 1 \frac{1}{4}

e) \frac{18}{19} : 6 = \frac{18}{19} \cdot \frac{1}{6} = \frac{18 \cdot 1}{19 \cdot 6} = \frac{3 \cdot 1}{19 \cdot 1} = \frac{3}{19}

Ответ:

а) 6 \frac{1}{2}

б) \frac{1}{12}

в) 15

г) 34

д) 1 \frac{1}{4}

е) \frac{3}{19}