How to add and subtract rational numbers in fraction form?

First you have to convert  the denominators to the Lowest Common Multiple (unless the denominators are equal, of course).

Example   1/4 + 1/2

The LCM of 2 and 4 = 4   so we can write 1/2  as 1*2/2*2 = 2/4. 
Now we can add:-
1/4 + 2/4 = 3/4.

Same thing goes for subtraction.

Example 2:-

5/6 - 1/7  :- 
LCM of 6 and 7  = 6*7 = 42  so we have:-
5*7 / 6*7   - 1*6 / 7*6  
= 35/42 - 6/42  =  29/42