let's firstly convert the mixed fractions to improper fractions, and then sum them up.
[tex]\bf \stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}}~\hfill \stackrel{mixed}{2\frac{1}{6}}\implies \cfrac{2\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{13}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{13}{4}+\cfrac{13}{6}\implies \stackrel{\textit{using the LCD of 12}}{\cfrac{(3)13+(2)13}{12}}\implies \cfrac{39+26}{12}\implies \cfrac{65}{12}\implies 5\frac{5}{12}[/tex]
