let's firstly convert all the mixed fractions to improper fractions and then sum them up.
[tex]\bf \stackrel{mixed}{4\frac{1}{12}}\implies \cfrac{4\cdot 12+1}{12}\implies \stackrel{improper}{\cfrac{49}{12}}~\hfill \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\\\ \stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\stackrel{improper}{\cfrac{11}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{49}{12}+\cfrac{9}{4}+\cfrac{11}{3}\implies \stackrel{\textit{using an LCD of 12}}{\cfrac{(1)49+(3)9+(4)11}{12}}\implies \cfrac{49+27+44}{12}\implies \cfrac{120}{12}\implies 10[/tex]
