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To add a mixed fraction like 2 \frac{1}{2} and  3\frac{1}{4} , you must express them first to 'improper fraction' (Just comment if you want to know how to express to 'improper fraction.).
The improper fraction of  2\frac{1}{2} is  \frac{5}{2}
and the improper fraction of  3\frac{1}{4} is  \frac{13}{4}

Then, you have to find the LCD (Least Common Denominator).  \frac{5}{2} and  \frac{13}{4} have the denominators 2 and 4. So, the LCD is 4, which can be divided by both denominators 2 and 4.

The first addend is  \frac{5}{2} , and we have to multiply both numerator and denominator by 2 to gain  \frac{10}{4} to have 4 as our new denominator.
The other addend will stay the same  \frac{13}{4} .

Now, we can add  \frac{10}{4}  \frac{13}{4} and is equal to  \frac{23}{4} . Just add the numerators and copy the denominator.

You can express your sum  \frac{23}{4} to mixed fraction and it will be  5\frac{3}{4} .
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Just add the whole numbers then find the LCD of the fraction. EZ