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A fraction p/q>=1. A fraction with p/q<1 is called a proper fraction. Therefore, the special cases 1/1, 2/2, 3/3, etc. are generally considered to be improper.

The simple continued fraction representations of e given by [2; 1, 2, 1, 1, 4, 1, 1, 6, ...] (OEIS A003417). This continued fraction is sometimes known as Euler's continued ...

A common fraction is a fraction in which numerator and denominator are both integers, as opposed to fractions. For example, 2/5 is a common fraction, while (1/3)/(2/5) is ...

The mathematical golden rule states that, for any fraction, both numerator and denominator may be multiplied by the same number without changing the fraction's value.

A fraction a/b written in lowest terms, i.e., by dividing numerator and denominator through by their greatest common divisor (a,b). For example, 2/3 is the reduced fraction ...

A rational number expressed in the form a/b (in-line notation) or a/b (traditional "display" notation), where a is called the numerator and b is called the denominator. When ...

An algorithm for computing an Egyptian fraction, called the Farey sequence method by Bleicher (1972).

Given a Farey sequence with consecutive terms h/k and h^'/k^', then the mediant is defined as the reduced form of the fraction (h+h^')/(k+k^').

An algorithm for computing an Egyptian fraction (Stewart 1992).

The nth partial denominator in a generalized continued fraction b_0+K_(n=1)^infty(a_n)/(b_n) or simple continued fraction b_0+K_(n=1)^infty1/(b_n) is the expression b_n. For ...