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A fraction is a division expression where both dividend and divisor are integers (typically called the numerator and denominator), and there is no implication that the division must be evaluated further. A second way to show division is to use the division sign (÷, also known as obelus though the term has additional meanings), common in ...
When the numerator and the denominator are both positive, the fraction is called proper if the numerator is less than the denominator, and improper otherwise. [11] The concept of an improper fraction is a late development, with the terminology deriving from the fact that fraction means piece , so a proper fraction must be less than 1. [ 10 ]
Beyond primary education, the symbol '÷' for division is seldom used, but is replaced by the use of algebraic fractions, [12] typically written vertically with the numerator stacked above the denominator – which makes grouping explicit and unambiguous – but sometimes written inline using the slash or solidus symbol '/'. [13]
A rational number can be defined as the quotient of two integers (as long as the denominator is non-zero). A more detailed definition goes as follows: [10] A real number r is rational, if and only if it can be expressed as a quotient of two integers with a nonzero denominator. A real number that is not rational is irrational.
A similar procedure is used for subtraction. If the two numbers do not have the same denominator then they must be transformed to find a common denominator. This can be achieved by scaling the first number with the denominator of the second number while scaling the second number with the denominator of the first 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. [1]