let's first off convert the mixed fractions to improper fractions, and then add, bearing in mind that the LCD from 4 and 8 is just 8.
[tex]\bf \stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}}~\hfill \stackrel{mixed}{1\frac{7}{8}}\implies \cfrac{1\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{15}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{11}{4}+\cfrac{15}{8}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(2)11~~+~~(1)15}{8}}\implies \cfrac{22+15}{8}\implies \cfrac{37}{8}\implies 4\frac{5}{8}[/tex]
