1) \(\left(\frac{17}{10} - \frac{1}{20}\right) \cdot \frac{4}{15} = ?\) 2) \(\left(\frac{10}{13} + \frac{15}{4}\right) \cdot \frac{26}{5} = ?\) 3) \(\left(\frac{3}{4} - \frac{1}{6}\right)^2 : 3 = ?\) 4) \(\left(\frac{2}{20} + \frac{1}{30}\right)^2 \cdot 15 = ?\)

Решение:

1. \(\left(\frac{17}{10} - \frac{1}{20}\right) \cdot \frac{4}{15} = \left(\frac{34}{20} - \frac{1}{20}\right) \cdot \frac{4}{15} = \frac{33}{20} \cdot \frac{4}{15} = \frac{33 \cdot 4}{20 \cdot 15} = \frac{33 \cdot 1}{5 \cdot 15} = \frac{11 \cdot 1}{5 \cdot 5} = \frac{11}{25}\)
2. \(\left(\frac{10}{13} + \frac{15}{4}\right) \cdot \frac{26}{5} = \left(\frac{40}{52} + \frac{195}{52}\right) \cdot \frac{26}{5} = \frac{235}{52} \cdot \frac{26}{5} = \frac{235 \cdot 26}{52 \cdot 5} = \frac{235 \cdot 1}{2 \cdot 5} = \frac{47 \cdot 1}{2 \cdot 1} = \frac{47}{2} = 23.5\)
3. \(\left(\frac{3}{4} - \frac{1}{6}\right)^2 : 3 = \left(\frac{9}{12} - \frac{2}{12}\right)^2 : 3 = \left(\frac{7}{12}\right)^2 : 3 = \frac{49}{144} : 3 = \frac{49}{144 \cdot 3} = \frac{49}{432}\)
4. \(\left(\frac{2}{20} + \frac{1}{30}\right)^2 \cdot 15 = \left(\frac{1}{10} + \frac{1}{30}\right)^2 \cdot 15 = \left(\frac{3}{30} + \frac{1}{30}\right)^2 \cdot 15 = \left(\frac{4}{30}\right)^2 \cdot 15 = \left(\frac{2}{15}\right)^2 \cdot 15 = \frac{4}{225} \cdot 15 = \frac{4 \cdot 15}{225} = \frac{4 \cdot 1}{15} = \frac{4}{15}\)

Ответ: 1) \(\frac{11}{25}\); 2) \(\frac{47}{2}\) или 23,5; 3) \(\frac{49}{432}\); 4) \(\frac{4}{15}\).