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The entire fraction may be expressed as a single composition, in which case it is hyphenated, or as a number of fractions with a numerator of one, in which case they are not. (For example, two-fifths is the fraction 2 / 5 and two fifths is the same fraction understood as 2 instances of 1 / 5 .) Fractions should always be ...
Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form =, where n is a given positive nonsquare integer, and integer solutions are sought for x and y. In Cartesian coordinates , the equation is represented by a hyperbola ; solutions occur wherever the curve passes through a point whose x and y ...
A continued fraction is a mathematical expression that can be written as a fraction with a denominator that is a sum that contains another simple or continued fraction. . Depending on whether this iteration terminates with a simple fraction or not, the continued fraction is finite or i
Slices of approximately 1/8 of a pizza. A unit fraction is a positive fraction with one as its numerator, 1/ n.It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number.
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.
The numerator and denominator are called the terms of the algebraic fraction. A complex fraction is a fraction whose numerator or denominator, or both, contains a fraction. A simple fraction contains no fraction either in its numerator or its denominator. A fraction is in lowest terms if the only factor common to the numerator and the ...
The proof is straightforward. From the fraction itself, one can construct the quadratic equation with integral coefficients that x must satisfy. Lagrange proved the converse of Euler's theorem: if x is a quadratic irrational, then the regular continued fraction expansion of x is periodic. [4]
The Rhind Mathematical Papyrus. 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.