A reduced fraction has coprime integers and positive denominator . Distinct reduced fractions with denominators at most differ by at least , since their difference has a nonzero integer numerator over a denominator at most .

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Reduced fraction by Ciro Santilli 40 Created 2024-07-12 Updated 2025-07-16
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A "reduced fraction" is a fraction that has the smallest possible integer numerator and denominator for its value.
For example:
(1)
is not a reduced fraction, because there is another fraction equal to it but with smaller numerator and denominator:
(2)
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