Fraction (mathematics)

In mathematics, a fraction is a quotient of numbers, like ³⁄₄, or more generally, an element of a quotient field.

The word is also used in related expressions, like continued fraction, see Special cases below.

For other, non-mathematical meanings of this word, see fraction.

Contents

1 Special cases

Special cases

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. Rational numbers are the quotient field of integers.

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 (absolute) value between 0 and 1;
improper fraction: a vulgar fraction with a (absolute) 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 10;
dyadic fraction: a vulgar fraction in which the denominator is a power of two.

Fractions which are rational numbers and could be written as vulgar fractions include:

A mixed fraction: A mixed fraction is an integer plus a proper fraction.
A compound fraction is a fraction where the numerator or denominator (or both) contain fractions.

Fractions which are not necessarily rational numbers include:

Let us end with the only example on this page where the "fraction" is not an element of a quotient field:

A continued fraction is an expression such as $a_0 + \frac{1}{a_1 + \frac{1}{a_2 + ...}}$ , where the a_i are integers.

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.

The contents of this article are licensed from Wikipedia.org under the GNU Free Documentation License. How to see transparent copy