\[\frac{4}{9} = \frac{40}{90};\ \ \ \frac{7}{15} = \frac{42}{90};\ \ \ \frac{23}{45} = \frac{46}{90};\ \]
\[\text{\ \ }\frac{13}{30} = \frac{39}{90}\]
\[\Rightarrow \frac{13}{30} < \ \ \frac{4}{9} < \ \frac{7}{15} < \ \ \frac{23}{45}.\]