\[a = 4\frac{2}{7};\ \ b = - 3\frac{3}{4}:\]
\[|a|\ :|b| = \left| 4\frac{2}{7} \right|:\left| - 3\frac{3}{4} \right| =\]
\[= \frac{30}{7}\ :\frac{15}{4} = \frac{30 \cdot 4}{7 \cdot 15} = \frac{8}{7} = 1\frac{1}{7}.\]