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Qué (quién) es fractions$29799$ - definición
FINITE SUM OF DISTINCT UNIT FRACTIONS
Egyptian fractions; Eqyption fraction; Egyptian Fractions; Sum of fractions
Unit fraction
![Fractions with tangent [[Ford circle]]s differ by a unit fraction](https://commons.wikimedia.org/wiki/Special:FilePath/Ford circles colour.svg?width=200 "Fractions with tangent [[Ford circle]]s differ by a unit fraction")
![The [[hydrogen spectral series]], on a logarithmic scale. The frequencies of the emission lines are proportional to differences of pairs of unit fractions.](https://commons.wikimedia.org/wiki/Special:FilePath/Hydrogen spectrum.svg?width=200 "The [[hydrogen spectral series]], on a logarithmic scale. The frequencies of the emission lines are proportional to differences of pairs of unit fractions.")
RATIONAL NUMBER WRITTEN AS A FRACTION WHERE THE NUMERATOR IS ONE AND THE DENOMINATOR IS A POSITIVE INTEGER
Unit fractions; Any rational number is a sum of unit fractions; Unit Fractions; Adjacent fractions
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n.
Clearing denominators
Clearing fractions
In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – which includes simple fractions.
Partial fraction decomposition
DECOMPOSITION OR PARTIAL FRACTION EXPANSION OF A MATHEMATICAL FUNCTION
Partial fractions in integration; Partial fraction decomposition over the reals; Partial fraction decomposition over R; Partial fractions; Partial Fraction Decomposition; Partial fraction expansion; Partial Fractions; Partial Fraction; Integration by partial fractions; Partial fractions decomposition; Method of partial fractions; Partial fraction
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
Wikipedia
Egyptian fraction
An Egyptian fraction is a finite sum of distinct unit fractions, such as
That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number ; for instance the Egyptian fraction above sums to . Every positive rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including and as summands, were used as a serious notation for rational numbers by the ancient Egyptians, and continued to be used by other civilizations into medieval times. In modern mathematical notation, Egyptian fractions have been superseded by vulgar fractions and decimal notation. However, Egyptian fractions continue to be an object of study in modern number theory and recreational mathematics, as well as in modern historical studies of ancient mathematics.