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In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers ; they may be taken in any field K .
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In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
[2] [3] Rational fractions are also known as rational expressions. A rational fraction () is called proper if < (), and improper otherwise. For example, the rational fraction is proper, and the rational fractions + + + and + + are improper. Any improper rational fraction can be expressed as the sum of a polynomial (possibly constant ...
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. [1 ...
In general, a common fraction is said to be a proper fraction if the absolute value of the fraction is strictly less than one—that is, if the fraction is greater than −1 and less than 1. [ 14 ] [ 15 ] It is said to be an improper fraction , or sometimes top-heavy fraction , [ 16 ] if the absolute value of the fraction is greater than or ...
Dyadic rationals in the interval from 0 to 1. In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not.
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