1. Вычислите: a) 1 \(\frac{1}{2}\) \(\cdot\) 1 \(\frac{1}{3}\); б) 1 \(\frac{1}{9}\) \(\cdot\) 3; в) 1 \(\frac{1}{9}\) \(\cdot\) 2 \(\frac{2}{5}\); г) 1 \(\frac{1}{8}\) : \(\frac{3}{4}\); д) 8 : 1 \(\frac{7}{9}\); е) 3 \(\frac{1}{2}\) : 1 \(\frac{1}{6}\);

Решение:

1. а) \(1 \frac{1}{2} \cdot 1 \frac{1}{3} = \frac{3}{2} \cdot \frac{4}{3} = \frac{3 \cdot 4}{2 \cdot 3} = \frac{12}{6} = 2\)
2. б) \(1 \frac{1}{9} \cdot 3 = \frac{10}{9} \cdot 3 = \frac{10 \cdot 3}{9} = \frac{30}{9} = \frac{10}{3} = 3 \frac{1}{3}\)
3. в) \(1 \frac{1}{9} \cdot 2 \frac{2}{5} = \frac{10}{9} \cdot \frac{12}{5} = \frac{10 \cdot 12}{9 \cdot 5} = \frac{120}{45} = \frac{8}{3} = 2 \frac{2}{3}\)
4. г) \(1 \frac{1}{8} : \frac{3}{4} = \frac{9}{8} : \frac{3}{4} = \frac{9}{8} \cdot \frac{4}{3} = \frac{9 \cdot 4}{8 \cdot 3} = \frac{36}{24} = \frac{3}{2} = 1 \frac{1}{2}\)
5. д) \(8 : 1 \frac{7}{9} = 8 : \frac{16}{9} = 8 \cdot \frac{9}{16} = \frac{8 \cdot 9}{16} = \frac{72}{16} = \frac{9}{2} = 4 \frac{1}{2}\)
6. е) \(3 \frac{1}{2} : 1 \frac{1}{6} = \frac{7}{2} : \frac{7}{6} = \frac{7}{2} \cdot \frac{6}{7} = \frac{7 \cdot 6}{2 \cdot 7} = \frac{42}{14} = 3\)

Ответ: а) 2; б) 3 \(\frac{1}{3}\); в) 2 \(\frac{2}{3}\); г) 1 \(\frac{1}{2}\); д) 4 \(\frac{1}{2}\); е) 3.