let's firstly convert the mixed fractions to improper fractions and then simply get their difference, our denominators will be 8 and 2, so our LCD will be 8.
[tex]\bf \stackrel{mixed}{27\frac{3}{8}}\implies \cfrac{27\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{219}{8}}~\hfill \stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{219}{8}-\cfrac{5}{2}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)219~~-~~(4)5}{8}}\implies \cfrac{219-20}{8}\implies \cfrac{199}{8}\implies 24\frac{7}{8}[/tex]
