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

1. Вычисляем:

1. а)
   

   \[ 1\frac{2}{3} \cdot 1\frac{1}{3} = \frac{5}{3} \cdot \frac{4}{3} = \frac{20}{9} = 2\frac{2}{9} \]

2. б)
   

   \[ 1\frac{9}{1} \cdot 3 = 10 \cdot 3 = 30 \]

3. в)
   

   \[ 1\frac{2}{5} \cdot 2\frac{5}{2} = \frac{7}{5} \cdot \frac{9}{2} = \frac{63}{10} = 6\frac{3}{10} \]

4. г)
   

   \[ 8 : 1\frac{7}{9} = 8 : \frac{16}{9} = 8 \cdot \frac{9}{16} = \frac{72}{16} = \frac{9}{2} = 4\frac{1}{2} \]

5. д)
   

   \[ 3\frac{1}{2} : 1\frac{6}{1} = \frac{7}{2} : 7 = \frac{7}{2} \cdot \frac{1}{7} = \frac{1}{2} \]

6. е)
   

   \[ 3\frac{1}{2} \cdot 1\frac{1}{3} + 3\frac{1}{2} \cdot 1\frac{1}{7} = \frac{7}{2} \cdot \frac{4}{3} + \frac{7}{2} \cdot \frac{8}{7} = \frac{28}{6} + \frac{56}{14} = \frac{14}{3} + 4 = 4\frac{2}{3} + 4 = 8\frac{2}{3} \]

Ответ: а) \(2\frac{2}{9}\), б) \(30\), в) \(6\frac{3}{10}\), г) \(4\frac{1}{2}\), д) \(\frac{1}{2}\), е) \(8\frac{2}{3}\)