[tex]3\frac{1}{2}\cdot \left(-2\frac{2}{7}\right)=\frac{7}{2}\cdot \left(-2\frac{2}{7}\right)=\frac{7}{2}\cdot \left(-\frac{16}{7}\right)=-\frac{16}{2}=\boxed{-8}[/tex]
[tex]\left(-4\cfrac{2}{7}\right)\div \left(-1\cfrac{1}{14}\right)=\left(-\cfrac{30}{7}\right)\div \left(-1\cfrac{1}{14}\right)=\left(-\cfrac{30}{7}\right)\div \left(-\cfrac{15}{14}\right)=\cfrac{\cfrac{30}{7}}{\frac{15}{14}}=\cfrac{30\cdot \:14}{7\cdot \:15}=\cfrac{2\cdot \:14}{7}=2\cdot \:2=\boxed{4}[/tex]