a)
[tex]3\frac{2}{3}+2\frac{3}{4}=3\frac{2\cdot4}{3\cdot4}+2\frac{3\cdot3}{4\cdot3}=3\frac{8}{12}+2\frac{9}{12}=5\frac{17}{12}=5+\frac{17}{12}=5+1\frac{5}{12}=6\frac{5}{12}\\[/tex]
b)
[tex]3\frac{1}{4}-1\frac{2}{3}=3\frac{1\cdot3}{4\cdot3}-1\frac{2\cdot4}{3\cdot4}=3\frac{3}{12}-1\frac{8}{12}=2\frac{15}{12}-1\frac{8}{12}=1\frac{7}{12}\\[/tex]