а) \(\frac{2}{9}\) числа \(6 \frac{3}{4}\); \(6 \frac{3}{4} = \frac{6 \cdot 4 + 3}{4} = \frac{27}{4}\)
\(\frac{2}{9} \cdot \frac{27}{4} = \frac{2 \cdot 27}{9 \cdot 4} = \frac{2 \cdot 9 \cdot 3}{9 \cdot 2 \cdot 2} = \frac{3}{2} = 1 \frac{1}{2}\)
б) \(\frac{6}{7}\) числа \(1 \frac{17}{18}\); \(1 \frac{17}{18} = \frac{1 \cdot 18 + 17}{18} = \frac{35}{18}\)
\(\frac{6}{7} \cdot \frac{35}{18} = \frac{6 \cdot 35}{7 \cdot 18} = \frac{6 \cdot 7 \cdot 5}{7 \cdot 6 \cdot 3} = \frac{5}{3} = 1 \frac{2}{3}\)
Ответ: а) \(1 \frac{1}{2}\), б) \(1 \frac{2}{3}\)