Answer :

[tex]1\dfrac{1}{4}+2\dfrac{1}{2}= 1\dfrac{1}{4}+2\dfrac{2}{4}=3\dfrac{3}{4}[/tex]
Write the fraction like this: 
[tex]1 \frac{1}{4}+ 2\frac{1}{2} = \frac{1\cdot4+1}{4} + \frac{2\cdot2+1}{2} = \frac{5}{4}+ \frac{5}{2} = \frac{5}{4} + \frac{5\cdot2}{2\cdot2}= \frac{5+10}{4} =\boxed{ \frac{15}{4} }[/tex]