How this calculation works
Generate the sorted Farey sequence, including its two endpoints.
THE FORMULA
List reduced fractions in [0,1] with denominator at most nA worked example
Order four gives 0/1, 1/4, 1/3, 1/2, 2/3, 3/4 and 1/1.
Good to know
Every fraction appears once in lowest terms.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Generate the sorted Farey sequence, including its two endpoints.
The primary result is labeled “Reduced fractions”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Every fraction appears once in lowest terms.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Order four gives 0/1, 1/4, 1/3, 1/2, 2/3, 3/4 and 1/1.
Which rule does this calculator apply?
List reduced fractions in [0,1] with denominator at most n