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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 .
In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression . Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms. As a third equivalent characterization, it is an infinite sequence of the form.
Description. The lowest common denominator of a set of fractions is the lowest number that is a multiple of all the denominators: their lowest common multiple. The product of the denominators is always a common denominator, as in: but it is not always the lowest common denominator, as in: Here, 36 is the least common multiple of 12 and 18.
In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, [ a] which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size. With the restricted definition, each Farey sequence starts with the value 0, denoted ...
The gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known for the values at rational points in general. Other fractional arguments can be approximated through efficient infinite products, infinite series ...
In mathematics, the Riemann zeta function is a function in complex analysis, which is also important in number theory. It is often denoted and is named after the mathematician Bernhard Riemann. When the argument is a real number greater than one, the zeta function satisfies the equation It can therefore provide the sum of various convergent ...
In mathematics, a percentage (from Latin per centum 'by a hundred') is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign (%), [ 1] although the abbreviations pct., pct, and sometimes pc are also used. [ 2] A percentage is a dimensionless number (pure number), primarily used for expressing proportions ...
Problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions. Problems 7–20 show how to multiply the expressions 1 + 1/2 + 1/4 = 7/4, and 1 + 2/3 + 1/3 = 2 by different fractions. Problems 21–23 are problems in completion, which in modern notation are simply subtraction problems.