Express the mixed number as a fraction:
[tex]4\frac{1}{2}=\frac{4\cdot2+1}{2}=\frac{8+1}{2}=\frac{9}{2}[/tex]Now, let's use the following formula to divide fractions:
[tex]\frac{a}{b}\div\frac{c}{d}=\frac{ad}{bc}[/tex]So:
[tex]\frac{9}{2}\div\frac{1}{8}=\frac{9\cdot8}{2\cdot1}=\frac{72}{2}=36[/tex][tex]\frac{9}{2}\div\frac{1}{4}=\frac{9\cdot4}{2\cdot1}=\frac{36}{2}=18[/tex][tex]\frac{9}{2}\div\frac{1}{6}=\frac{9\cdot6}{2\cdot1}=\frac{54}{2}=27[/tex]