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

1. Вычислим:

1. а) \( 2\frac{1}{2} \cdot 1\frac{1}{3} = \frac{5}{2} \cdot \frac{4}{3} = \frac{5 \cdot 4}{2 \cdot 3} = \frac{20}{6} = 3\frac{2}{6} = 3\frac{1}{3} \)
2. б) \( 1\frac{1}{9} \cdot 3 = \frac{10}{9} \cdot 3 = \frac{10 \cdot 3}{9} = \frac{30}{9} = 3\frac{3}{9} = 3\frac{1}{3} \)
3. в) \( 1\frac{1}{3} \cdot 3 = \frac{4}{3} \cdot 3 = \frac{4 \cdot 3}{3} = 4 \)
4. г) \( 8\frac{1}{7} : \frac{1}{9} = \frac{57}{7} : \frac{1}{9} = \frac{57}{7} \cdot 9 = \frac{57 \cdot 9}{7} = \frac{513}{7} = 73\frac{2}{7} \)
5. д) \( 1\frac{3}{5} : 2\frac{1}{5} = \frac{8}{5} : \frac{11}{5} = \frac{8}{5} \cdot \frac{5}{11} = \frac{8 \cdot 5}{5 \cdot 11} = \frac{8}{11} \)
6. е) \( 3\frac{1}{2} : 1\frac{1}{6} = \frac{7}{2} : \frac{7}{6} = \frac{7}{2} \cdot \frac{6}{7} = \frac{7 \cdot 6}{2 \cdot 7} = \frac{6}{2} = 3 \)