Search results
Results from the WOW.Com Content Network
In elementary algebra, root rationalisation (or rationalization) is a process by which radicals in the denominator of an algebraic fraction are eliminated.. If the denominator is a monomial in some radical, say , with k < n, rationalisation consists of multiplying the numerator and the denominator by , and replacing by x (this is allowed, as, by definition, a n th root of x is a number that ...
In the proof so far, the purpose for introducing the inequality in #1 comes from intuition that = = (the geometric series formula); therefore, if an inequality can be found from = +! that introduces a series with (b−1) in the numerator, and if the denominator term can be further reduced from ! to , as well as shifting the series indices from ...
In either case, all integers in the sequence, other than the first, must be positive. The integers are called the coefficients or terms of the continued fraction. [1] Simple continued fractions have a number of remarkable properties related to the Euclidean algorithm for integers or real numbers.
In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. [1] Consequently, any prime number that divides a does not divide b, and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. [2] One says also a is prime to b or a ...
is the ratio of two polynomials with complex coefficients, where Q is not the zero polynomial and P and Q have no common factor (this avoids f taking the indeterminate value 0/0). The domain of f is the set of complex numbers such that Q ( z ) ≠ 0 {\displaystyle Q(z)\neq 0} .
Two fractions a / b and c / d are equal or equivalent if and only if ad = bc.) 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 ...
Real numbers were called "proportions", being the ratios of two lengths, or equivalently being measures of a length in terms of another length, called unit length. Two lengths are "commensurable", if there is a unit in which they are both measured by integers, that is, in modern terminology, if their ratio is a rational number .
A least common multiple of a and b is a common multiple that is minimal, in the sense that for any other common multiple n of a and b, m divides n. In general, two elements in a commutative ring can have no least common multiple or more than one. However, any two least common multiples of the same pair of elements are associates. [10]