In common usage a fraction is any part of a unit.
A vulgar fraction is a rational number written as one integer (the numerator) divided by a non-zero integer (the denominator). Sub-categories of vulgar fraction include
- Irreducible fraction: a vulgar fraction "in lowest terms", where the numerator is an integer, the denominator is a positive integer, and the highest common factor of the numerator and the denominator is 1.
- Proper fraction: A vulgar fraction with a value between zero and one
- Improper fraction: A vulgar fraction with a value greater than 1.
- Unit fraction: A vulgar fraction with a numerator of 1.
- Egyptian fraction: The sum of distinct unit fractions.
- Decimal fraction: A vulgar fraction where the denominator is a power of ten.
- Dyadic fraction: A vulgar fraction in which the denominator is a power of two.
An irrational fraction or irrational number is a fraction which is not rational i.e. cannot be expressed as a vulgar fraction.
A continued fraction is an expression such as:
-
whre the ai are positive integers.
A compound fraction is a fraction where the numerator or denominator (or both) contain fractions.
Partial fractions can be used to decompose a rational function.
