Not necessarily. Strictly mathematically a (non-negative) fraction q/p is just the equivalence class of all non-negative integer pairs (s, t), t != 0, such that

Not necessarily. Strictly mathematically a (non-negative) fraction q/p is just the equivalence class of all non-negative integer pairs (s, t), t != 0, such that qt = sp As such we may make q as small as possible by finding a representative in the equivalence class where the numerator is smallest (using the well ordering principle of the of the natural numbers). You can identify this pair uniquely (when the fraction is not 0) by using divisibility but that isn't required here.