let's firstly convert the mixed fractions to improper fractions and then sum them up.
[tex]\bf \stackrel{mixed}{2\frac{2}{8}}\implies \cfrac{2\cdot 8+2}{8}\implies \stackrel{improper}{\cfrac{18}{8}}~\hfill \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{18}{8}+\cfrac{9}{4}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)18+(2)9}{8}}\implies \cfrac{18+18}{8}\implies \cfrac{36}{8}\implies \cfrac{9}{2}\implies 4\frac{1}{2}[/tex]
