let's convert the mixed fractions to improper fractions firstly.
[tex]\bf \stackrel{mixed}{2\frac{3}{8}}\implies \cfrac{2\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{19}{8}}~\hfill \stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}} \\\\\\ \stackrel{mixed}{3\frac{1}{8}}\implies \cfrac{3\cdot 8+1}{8}\implies \stackrel{improper}{\cfrac{25}{8}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{19}{8}-\cfrac{9}{2}+\cfrac{25}{8}-\cfrac{1}{2}\implies \stackrel{\textit{using an LCD of 8}}{\cfrac{(1)19-(4)9+(1)25-(4)1}{8}}\implies \cfrac{19-36+25-4}{8} \\\\\\ \cfrac{4}{8}\implies \cfrac{1}{2}[/tex]
