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No, you do not need to find a common denominator when multiplying fractions. To multiply fractions, you simply multiply the numerators together and the denominators together. However, finding a common denominator can be helpful when simplifying the resulting fraction.
You don't need a common denominator to divide fractions.
Adding like terms can be like adding fractions. You can only add fractions with a common denomonator. You can only combine terms together if they are like. Think of like terms as denomonators. You can only add if they are like.
you flip the last (second) fraction, and then you change the divide sign into a times sign. You can then times the fractions from there. You do not need the same denominator to times fractions.
You don't need a common denominator to divide fractions.