#### Answer

$\frac{1}{2}$

#### Work Step by Step

$\frac{7}{8}\div\frac{1}{4}\times\frac{1}{7}$
$=\frac{7}{8}\times\frac{4}{1}\times\frac{1}{7}$
$=\frac{1}{8}\times\frac{4}{1}\times\frac{1}{1}$
$=\frac{1}{2}\times\frac{1}{1}\times\frac{1}{1}$
$=\frac{1}{2}$