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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 .
Continued fraction. A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this ...
An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). [ 1] In other words, a fraction a b is irreducible if and only if a and b are coprime, that ...
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator p and a non-zero denominator q. [ 1] For example, is a rational number, as is every integer (e.g., ). The set of all rational numbers, also referred to as " the rationals ", [ 2] the field of rationals[ 3 ...
Algebraic fraction. In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions. Two examples of algebraic fractions are and . Algebraic fractions are subject to the same laws as arithmetic fractions . A rational fraction is an algebraic fraction whose numerator and denominator are both polynomials.
Clearing denominators. 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 .
Algebraic form. Continued fraction. The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5. It is more precisely called the principal square root of 5, to distinguish it from the negative number with the same property. This number appears in the fractional expression for the golden ratio.
Conversely the period of the repeating decimal of a fraction c / d will be (at most) the smallest number n such that 10 n − 1 is divisible by d. For example, the fraction 2 / 7 has d = 7, and the smallest k that makes 10 k − 1 divisible by 7 is k = 6, because 999999 = 7 × 142857. The period of the fraction 2 / 7 is ...
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