Solution:
To evaluate:
[tex]4\frac{1}{6}-\frac{8}{9}[/tex]we have
[tex]\begin{gathered} Convert\text{ to improper fraction,} \\ \frac{(6\times4)+1}{6}-\frac{8}{9} \\ \Rightarrow\frac{25}{6}-\frac{8}{9} \\ LCM\text{ is 36, thus} \\ \frac{6(25)-4(8)}{36}=\frac{150-32}{36} \\ =\frac{118}{36} \\ =3\frac{5}{18} \end{gathered}[/tex]Hence, we have
[tex]3\frac{5}{18}[/tex]