irreducible fraction

Every positive rational number can be represented as an irreducible fraction in exactly one way.

The final result, /, is an irreducible fraction because 4 and 3 have no common factors other than 1.

Therefore the square of an irreducible fraction cannot be reduced to an integer.

One half, an irreducible fraction resulting from dividing one by two.

Drill bit sizes are written down on paper and etched onto bits as irreducible fractions.

This is the smallest star polygon that can be drawn in two forms, as irreducible fractions.

For example, , , and are all irreducible fractions.

The contrapositive of this statement is "If cannot be expressed as an irreducible fraction, then it is not rational".

These integers allow to define the rational numbers, which are irreducible fractions of two integers.

Every rational number has a unique representation as an irreducible fraction with a positive denominator (however although both are irreducible).

In particular, Goodwyn wanted to tabulate the decimal values for all irreducible fractions with denominators less than or equal to 1,024.

The irreducible fraction for a given element is unique up to multiplication of denominator and numerator by the same invertible element.

In higher mathematics, "irreducible fraction" may also refer to rational fractions such that the numerator and the denominator are coprime polynomials.

Therefore, if it can be proven that cannot be expressed as an irreducible fraction, then it must be the case that is not a rational number.

In mathematics, a Ford circle is a circle with center at and radius where is an irreducible fraction, i.e. and are coprime integers.

An irreducible fraction (or fraction in lowest terms) is a vulgar fraction in which the numerator and denominator are smaller than those in any other equivalent fraction.

The fact that any rational number has a unique representation as an irreducible fraction is utilized in various proofs of the irrationality of the square root of 2 and of other irrational numbers.

An irreducible fraction is one that is visible from the origin; the action of the modular group on a fraction never takes a visible (irreducible) to a hidden (reducible) one, and vice versa.

An irreducible fraction (or fraction in lowest terms or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and -1, when negative numbers are considered).

In the case of the rational numbers this means that any number has two irreducible fractions, related by a change of sign of both numerator and denominator; this ambiguity can be removed by requiring the denominator to be positive.

As explained in recurring decimals, whenever an irreducible fraction is written in radix point notation in any base, the fraction can be expressed exactly (terminates) if and only if all the prime factors of its denominator are also prime factors of the base.

All other prime factors, except 2, are not shared by either ten or twelve, so they do not influence the relative likeliness of encountering recurring digits (any irreducible fraction that contains any of these other factors in its denominator will recur in either base).

The notion of irreducible fraction generalizes to the field of fractions of any unique factorization domain: any element of such a field can be written as a fraction in which denominator and numerator are coprime, by dividing both by their greatest common divisor.