Given an unreduced fraction, one may reduce it by cancelling common factors of the numerator and denominator in accordance with the rules of arithmetic. For example, is not a reduced fraction because both 15 and 27 are divisible by 3. So in order to reduce, we write , and 5 and 9 are relatively prime, so this fraction is reduced.
Sometimes, it might take several steps to reduce a fraction (because we don't notice all the common factors of the numerator and denominator, for example). For instance, in reducing the fraction , we might first notice that the numerator and denominator are divisble by 3 and so reduce to . We have now reduced our original fraction, but it can be reduced further: both 119 and 91 are divisble by 7, and the fraction reduces again to . In this case, we call the intermediate steps partially reduced and the final, reduced fraction fully reduced.
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