You may have multiplied by $\displaystyle\frac{{1}}{{6}}\usepackage{cmbright}\Huge\$ instead of its reciprocal.

$\displaystyle\frac{{2}}{{9}}\div\frac{{1}}{{6}}=\frac{{2}}{{9}}\cdot\frac{{6}}{{1}}=\frac{{12}}{{9}}={1}\frac{{1}}{{3}}\usepackage{cmbright}\Huge\$