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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 is ...
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 .
A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . A continued fraction is a mathematical expression that can be writen 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 ...
This is denoted as 20 / 5 = 4, or 20 / 5 = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is the quotient. Unlike the other basic operations, when dividing natural numbers there is sometimes a remainder that will not go evenly into the dividend; for example, 10 / 3 leaves a remainder of 1, as 10 is not a multiple of 3.
If the ratio consists of only two values, it can be represented as a fraction, in particular as a decimal fraction. For example, older televisions have a 4:3 aspect ratio, which means that the width is 4/3 of the height (this can also be expressed as 1.33:1 or just 1.33 rounded to two decimal places). More recent widescreen TVs have a 16:9 ...
The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. This quadratic polynomial has two roots, and. The golden ratio is also closely related to the polynomial. which has roots and As the root of a quadratic polynomial, the golden ratio is a constructible number.
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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]