A way to address this is to learn how to compare fractions and find common denominators so that two fractions can be numerically compared clearly. The worksheets on this page provide exercises to do exactly that, and they are good practice for the steps necessary for other fraction operations.
Subtracting fractions is similar to adding fractions. Most of the work involves the denominator. If the denominators of the two fractions are already the same, much of the work is done. Simply subtract the two numerators to get the answer fraction using the same denominator, and then reduce and make a proper fraction.