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Yes. You need common denominators if you want to:Add fractionsSubtract fractionsCompare fractions ("which is larger?")You do not need common denominators to multiply or divide fractions. Thus, in the case of fractions, multiplication and division is actually easier than addition and subtraction.
You can add or subtract fractions only if they are "like" fractions, that is, only if they have the same denominator - unless you know your fractions really well.
You don't need a common denominator to divide fractions.
Similar fractions are fractions with the same denominator. In order to add or subtract fractions they need to be similar.