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Reduced fraction

Ciro Santilli (@cirosantilli, 37) ... Mathematics Area of mathematics Formalization of mathematics Number Rational number Fraction
Created 2024-07-12 Updated 2025-07-16  0 By others on same topic  0 Discussions Create my own version
A "reduced fraction" is a fraction that has the smallest possible integer numerator and denominator for its value.
For example:
63​
(1)
is not a reduced fraction, because there is another fraction equal to it but with smaller numerator and denominator:
21​
(2)
  • Table of contents
    • Farey sequence Reduced fraction
      • Farey sunburst Farey sequence
    • Number of elements in a Farey sequence Reduced fraction

Farey sequence (Fn​)

 1  0
Reduced fraction

Farey sunburst

 0  0
Farey sequence
en.wikipedia.org/w/index.php?title=Farey_sequence&oldid=1223364653#Farey_sunburst

Number of elements in a Farey sequence

 0  0
Reduced fraction
en.wikipedia.org/w/index.php?title=Farey_sequence&oldid=1223364653#Sequence_length_and_index_of_a_fraction
∣Fn​∣=1+Φ(n)
(1)
where Φ(n) is the totient summatory function.

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