It depends on the fraction. For me, "1/2" usually originates because I want to take half of something... But seriously, fractions have been around as far back as ancient Egypt. Checkout: http://en.wikipedia.org/wiki/Fraction_(mathematics)#History
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A prefecture of origin is the region or area within a country where a person is from. So the western region would be the prefecture of Origin if a person was from Maharashtra, India.
you need the azure flute because arceus lives in the hall of origin.
No.
Renaming a fraction, if done properly, will not affect its size.
3