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Fractions are distinct from rational numbers because they are a representation: $\frac 34$ and $\frac{30}{40}$ are different fractions that happen to represent the same rational number. Questions about fractions may also also include algebraic expressions of the form $\frac pq$, continued fractions, arithmetic with fractions, operations on rational functions, the field of quotients of a ring, and possibly even certain questions about Legendre series or Möbius transformations.

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