$因为\frac{1} {2} = \frac{172} {344}, ,\frac{199} {344} > \frac{172} {344},$
$所以\frac{199} {344} > \frac{1} {2};$
$又 因为\frac{1} {2} = \frac{144} {288}, \frac{111} {288} < \frac{144} {288},$
$所以\frac{111} {288}<\frac{1}{2},所以 \frac{199} {344} > \frac{111} {288}。$