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What is the formal definition of fraction?

Everyone says something different.

Thank you for your answers.

rain
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    You have formal definition of rational numbers, not sure about fractions. – King Tut Feb 27 '18 at 15:30
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    That's because there is no formal definition of fraction! It's a term that lots of different people use in lots of different (albeit very related) ways. – Billy Feb 27 '18 at 15:31
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    Related: Is $\frac{1}{\sqrt{2}}$ a fraction or not?. – StackTD Feb 27 '18 at 15:32
  • "Everyone says something different". This raises the question of what they say, because either you are speaking to one of those people right now - in which case he will alwas say one of those different things you aren't satisfied with - or you are speaking to someone else who can't possibly know what they said to you. –  Feb 27 '18 at 15:37

1 Answers1

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Yes, in abstract algebra the concept of localization provides a formal definition of a fraction. In short a fraction is an ordered pair $(a,b)$ (usually expressed $\frac{a}{b}$), along with the equivalence $(a,b) = (c,d)$ if $ad=bc$.

Jonathan
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