Answer :
well, is just their difference, let's first convert the mixed fraction to "improper" and then subtract.
[tex]\bf \stackrel{mixed}{1\frac{1}{8}}\implies \cfrac{1\cdot 8+1}{8}\implies \stackrel{improper}{\cfrac{9}{8}}\\\\ -------------------------------\\\\ \cfrac{9}{8}-\cfrac{3}{4}\impliedby \textit{our LCD is then 8}\implies \cfrac{(1\cdot 9)~~-~~(2\cdot 3)}{8} \\\\\\ \cfrac{9-6}{8}\implies \cfrac{3}{8}[/tex]
[tex]\bf \stackrel{mixed}{1\frac{1}{8}}\implies \cfrac{1\cdot 8+1}{8}\implies \stackrel{improper}{\cfrac{9}{8}}\\\\ -------------------------------\\\\ \cfrac{9}{8}-\cfrac{3}{4}\impliedby \textit{our LCD is then 8}\implies \cfrac{(1\cdot 9)~~-~~(2\cdot 3)}{8} \\\\\\ \cfrac{9-6}{8}\implies \cfrac{3}{8}[/tex]