A fraction is division. For example, the fraction 2/3 is a cleaner way of writing 2 divided by 3, the answer to which is .666666. The purpose of fractions is not having to deal with decimals and having a cleaner way to write numbers.
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No, You only need a common denominator when adding or subtracting fractions.
Because it is not how multiplication or division are defined.
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.
Fractions are representations of division. The line in a fraction can be read as "divided by." 3/4 = 3 divided by 4
Indeed--fractions are merely an alternative way to represent division. example: 1/2 ----> one divided by two ----> 0.5 ;)