Answer:
[tex]\frac{9}{6}[/tex]
Step-by-step explanation:
The given fractions are;
[tex]\frac{23}{8},\frac{11}{2},\frac{9}{6},\frac{15}{7}[/tex]
The least common denominator is [tex]168[/tex].
We express all the fractions in equivalent form with the LCD as the denominator.
[tex]\frac{23}{8}=\frac{21\times23}{21\times8}=\frac{483}{168}[/tex]
[tex]\frac{11}{2}=\frac{84\times11}{84\times2}=\frac{924}{168}[/tex]
[tex]\frac{9}{6}=\frac{28\times9}{28\times6}=\frac{252}{168}[/tex]
[tex]\frac{15}{7}=\frac{24\times15}{24\times7}=\frac{360}{168}[/tex]
We now compare the equivalent forms and arrange from the least to the greatest.
[tex]\frac{252}{168}\:<\:\frac{360}{168}\:<\:\frac{483}{168}\:<\:\frac{924}{168}[/tex]
This implies that,
[tex]\frac{9}{6}\:<\:\frac{15}{7}\:<\:\frac{23}{8}\:<\:\frac{11}{2}[/tex]
Therefore the first would be [tex]\frac{9}{6}[/tex].
