\[\boxed{\text{5.503.}}\]
\[\textbf{а)}\ \frac{3}{4} \cdot \frac{4}{15} = \frac{3 \cdot 4}{4 \cdot 15} = \frac{1}{5}\]
\[\textbf{б)}\ 7 \cdot \frac{3}{7} = \frac{7 \cdot 3}{7} = 3\]
\[\textbf{в)}\ \frac{3}{8} \cdot \frac{1}{3} = \frac{3}{8 \cdot 3} = \frac{1}{8}\]
\[\textbf{г)}\ \left( \frac{1}{6} + \frac{1}{6} + \frac{1}{6} \right) \cdot \frac{2}{5} = \frac{3}{6} \cdot \frac{2}{5} = \frac{6}{30} =\]
\[= \frac{1}{5}\]