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B What is the name of this type of fraction

  1. Nov 19, 2016 #1
    Take the fractions 2/5 and 4/10. 2/5 cannot be simplified further without converting the integers into decimals. I need to know the name of the 2/5 fraction. Maybe it's called irreducible form or something like that. Let me give another example, of 1/3, 3/9, or 33/99 only 1/3 is irreducible because to divide the numerator and the denominator would turn it into a decimal.
     
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  3. Nov 19, 2016 #2

    andrewkirk

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    I would just call the fraction 'irreducible', ie I would say 2/5 is an irreducible fraction and 4/10 is not (we could say it is a 'reducible fraction'). I would not bother adding 'form' because in common usage a fraction is a representation of a (rational) number, rather than a number itself. So that 2/5 and 4/10 are different fractions, both of which represent the same rational number.

    Set theoretically, it is convenient to define a rational number as an equivalence class of elements of ##\mathbb Z\times\mathbb N##, under the equivalence relation ##=_{\mathbb Q}## such that ##(a,b)=_{\mathbb Q} (c,d)## iff ##a/b=c/d##. The equivalence class is a rational number. The elements of the equivalence class are fractions, where the fraction ##(a,b)## is formally written as ##\frac ab##, and that fraction is irreducible iff the greatest common factor of ##a## and ##b## is 1.
     
    Last edited: Nov 19, 2016
  4. Nov 19, 2016 #3
    Thanks. I appreciate you taking the time to help me out.
     
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