$\frac{4}{9}<x<\frac{5}{9}$
$\frac{4}{9}=\frac{8}{18}=\frac{12}{27}$
$\frac{5}{9}=\frac{10}{18}=\frac{15}{27}$
$\frac{8}{18}<x<\frac{10}{18}$
$x=\frac{9}{18}=\frac{1}{2}$
$\frac{12}{27}<x<\frac{15}{27}$
$x=\frac{14}{27}$
Ответ: $\frac{1}{2},\frac{14}{27}$.

$\frac{1}{8}<x<\frac{1}{7}$
$\frac{1}{8}=\frac{7}{56}=\frac{14}{112}=\frac{28}{224}$
$\frac{1}{7}=\frac{8}{56}=\frac{16}{112}=\frac{32}{224}$
$\frac{14}{112}<x<\frac{16}{112}$
$x=\frac{15}{112}$
$\frac{28}{224}<x<\frac{32}{224}$
$x=\frac{29}{224}$
Ответ: $\frac{15}{112},\frac{29}{224}$.