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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.
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.
To add fractions containing unlike quantities (e.g. quarters and thirds), it is necessary to convert all amounts to like quantities. It is easy to work out the chosen type of fraction to convert to; simply multiply together the two denominators (bottom number) of each fraction. In case of an integer number apply the invisible denominator 1.
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 Rhind Mathematical Papyrus. An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number ; for ...
Addition of fractions is much simpler when the denominators are the same; in this case, one can simply add the numerators while leaving the denominator the same: + = +, so + = + =. [ 63 ] The commutativity and associativity of rational addition is an easy consequence of the laws of integer arithmetic. [ 64 ]
An interesting feature of ancient Egyptian mathematics is the use of unit fractions. [7] The Egyptians used some special notation for fractions such as 1 / 2 , 1 / 3 and 2 / 3 and in some texts for 3 / 4 , but other fractions were all written as unit fractions of the form 1 / n or sums of such unit ...
Mediant (mathematics) In mathematics, the mediant of two fractions, generally made up of four positive integers. and is defined as. That is to say, the numerator and denominator of the mediant are the sums of the numerators and denominators of the given fractions, respectively. It is sometimes called the freshman sum, as it is a common mistake ...
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