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Hello,
I've just added another example in the description and also a few more tests (including random ones).
Hi Giacomo,
You can find the two definitions on Wolfram MathWorld:
http://mathworld.wolfram.com/ProperFraction.html
http://mathworld.wolfram.com/ReducedFraction.html
I think the definition is incorrect. A proper fraction is a fraction that is less than one while a reduced fraction is a fraction whose numerator and denominator are coprimes.