This site is supported by donations to The OEIS Foundation.
If the numerator and the denominator are coprime, then the fraction is said to be in reduced form, i.e. written in lowest terms. For example, . If , the fraction is greater than 1, in which case it might be rewritten as . For example, , though generally the addition sign becomes a tacit operator.
One important sequence of fractions is the sequence of even-index Bernoulli numbers
In the OEIS, sequences of fractions are generally rendered as two sequences of integers, one for the numerator, the other for the denominator. Both sequences then have Keyword frac and cross-references to each other. In the Bernoulli example, A000367 gives the numerators and A002445 gives the denominators.
Proper, improper and mixed fractions
Fractions are either
- Proper fractions: fractions s.t. ;
- Improper fractions: fractions s.t. ;
- Mixed fractions: fractions s.t. and .
- Rational numbers
- Index to fractions in OEIS
- Unit fractions
- Egyptian fractions
- Continued fractions