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6 1 2 1 1 −1 4 5 9. and would be written in modern notation as 6 1 / 4 , 1 1 / 5 , and 2 − 1 / 9 (i.e., 1 8 / 9 ). The horizontal fraction bar is first attested in the work of Al-Hassār (fl. 1200), [35] a Muslim mathematician from Fez, Morocco, who specialized in Islamic inheritance jurisprudence.
By default, the output value is rounded to adjust its precision to match that of the input. An input such as 1234 is interpreted as 1234 ± 0.5, while 1200 is interpreted as 1200 ± 50, and the output value is displayed accordingly, taking into account the scale factor used in the conversion.
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 of 2 / 4 . A fraction that is reducible can be reduced by dividing both the numerator ...
Because of the identity property of multiplication, multiplying any quantity (physical or not) by the dimensionless 1 does not change that quantity. [5] Once this and the conversion factor for seconds per hour have been multiplied by the original fraction to cancel out the units mile and hour, 10 miles per hour converts to 4.4704 metres per second.
In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
If x 2 is the remaining fraction after this step of the greedy expansion, it satisfies the equation P 1 (x 2 + 1 / 2 ) = 0, which can be expanded as P 2 (x 2) = 4x 2 2 + 8x 2 − 1 = 0. Since P 2 (x) < 0 for x = 1 / 9 , and P 2 (x) > 0 for all x > 1 / 8 , the next term in the greedy expansion is 1 / 9 .
The script ASCIIMathML.js is freely available under the MIT License. [4] The latest version also includes support for SVG graphics, natively in Mozilla Firefox and via a plug-in in IE7 . Per May 2009 there is a new version available.