Fractions

In common usage a fraction is any part of a unit.

In mathematics:

• A vulgar fraction is a rational number written as one integer (the numerator) divided by a non-zero integer (the denominator). The line that separates the numerator and the denominator is called the Vinculum. 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.
• A Mixed fraction: A mixed fraction is an integer plus a proper fraction.
• An irrational fraction is, if all fractions must be capable of being expressed as a vulgar fraction, a contradiction in terms. An irrational number is, by definition, not rational i.e. it cannot be expressed as a vulgar fraction.
• A continued fraction is an expression such as:

<math>x = a_0 + \frac{1}{a_1 + \frac{1}{a_2 + \frac{1}{a_3+\dots}}} <math>

where the a_i 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.

In religion:

• In some Christian denominations, the Fraction is the ceremonial act of breaking the bread during Communion.