fraction

Other Definitions
fraction (dict)

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 the 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.

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

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.
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.
In Primary Schools, fractions have been demonstrated through Cuisenaire rods.

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

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