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Reducing FractionsReducing fractions is too important a topic in algebra and I will come again over it. But for now, understand that this (in the end, simple) operation is carried out to actually help you! ... and simplify your (or a mathematician's, a scientist's, an accountant's) life. To help you drop unnecessary cargo.. Yes, many things that at first you don't quite understand and find meaningless, are just tools to make maths easier!
Reducing fractions simply means to find a way to deal with smaller numbers without loosing the same proportion of the original fraction. In other words it means to find an equivalent fraction where the numerator and denominator are as small as possible.
...and the way to do it is simply by finding the Greatest Common Factor (GCF) between two or more numbers. That's why the teacher at school started making you look at number in different ways, to speak about division, divisibility rules and prime numbers. Here is an example (if you don't know how to multiply fractions click here). Note that the 5's eliminate each others because 5:5=1 and so you can consider them as redundant (multiplication by 1 leave any product unaffected). By the way the "trick" of finding the "ones" in mathematics and in algebra is a very important and enormously used strategy!
1550. Mathematics is the most powerful instrument which we Treatise on Infinitesimal Calculus (Oxford,
source: Memorabilia mathematica; or, The philomath's quotationbook  Moritz, Robert Édouard, 18681940

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