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A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [ 9] As with other fractions, the denominator ( b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
For example, 1 / 4 , 5 / 6 , and −101 / 100 are all irreducible fractions. On the other hand, 2 / 4 is reducible since it is equal in value to 1 / 2 , and the numerator of 1 / 2 is less than the numerator of 2 / 4 . A fraction that is reducible can be reduced by dividing both the numerator ...
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]
Number Forms is a Unicode block containing Unicode compatibility characters that have specific meaning as numbers, but are constructed from other characters. They consist primarily of vulgar fractions and Roman numerals. In addition to the characters in the Number Forms block, three fractions (¼, ½, and ¾) were inherited from ISO-8859-1 ...
4 / 7 = 4 × 0. 142857 = 0. 571428 5 / 7 = 5 × 0. 142857 = 0. 714285 6 / 7 = 6 × 0. 142857 = 0. 857142; The reason for the cyclic behavior is apparent from an arithmetic exercise of long division of 1 / 7 : the sequential remainders are the cyclic sequence {1, 3, 2, 6, 4, 5}. See also the article 142,857 for ...
Fibonacci sometimes wrote several fractions next to each other, representing a sum of the given fractions. For instance, 1/3+1/4 = 7/12, so a notation like would represent the number that would now more commonly be written as the mixed number , or simply the improper fraction . Notation of this form can be distinguished from sequences of ...
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [ 1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [ 2] Since the problem had withstood the attacks ...
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 denominator is 1. An expression which is not in fractional form is an integral ...