[tex]1\frac{1}{4} : \frac{2}{9} = \frac{4\ \cdot\ 1\ +\ 1}{4} : \frac{2}{9} =\frac{5}{4} : \frac{2}{9} = \frac{5}{4} \cdot \frac{9}{2} = \frac{45}{8} = \boxed{5\frac{5}{8}}[/tex]
