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For example, when adding and the single denominators have a common factor 2, and therefore, instead of the denominator 24 (4 × 6), the halved denominator 12 may be used, not only reducing the denominator in the result, but also the factors in the numerator.
It is usually easiest to add, subtract, or compare fractions when each is expressed with the same denominator, called a "common denominator". For example, the numerators of fractions with common denominators can simply be added, such that + = and that <, since each fraction has the common denominator 12.
In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
A style guide, or style manual, is a set of standards for the writing and design of documents, either for general use or for a specific publication, organization or field. The implementation of a style guide provides uniformity in style and formatting within a document and across multiple documents.
Every decimal representation of a rational number can be converted to a fraction by converting it into a sum of the integer, non-repeating, and repeating parts and then converting that sum to a single fraction with a common denominator. For example, to convert ¯ to a fraction one notes the lemma: ¯ = ¯ = ¯ = = = ()
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A famous example for lexical ambiguity is the following sentence: "Wenn hinter Fliegen Fliegen fliegen, fliegen Fliegen Fliegen hinterher.", meaning "When flies fly behind flies, then flies fly in pursuit of flies." [40] [circular reference] It takes advantage of some German nouns and corresponding verbs being homonymous. While not noticeable ...
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