There are different ways to solve this problem.
-You can turn 4 1/4 and 2 1/4 into decimal form and add them together.
-Turn them both into improper fractions (for example using 4 1/4, its the denominator of the fraction times the big number and added to the numerator. This is all over the original denominator. In practice it 4 x 4=16 +1=17, so the improper fraction is 17/4 (which is the same as 4 1/4)) and then add them together.
Just don't forgot that you can only add fractions correctly that have the same denominator in the written form (1/4 +1/4 vs 1/7 + 1/4) and to simply your answer if it can be reduced.
Hope this helps!