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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 and denominator by a common factor.
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.
Continued fraction. A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this ...
Each generator halves the number of runs required. A design with p such generators is a 1/(l p)=l −p fraction of the full factorial design. For example, a 2 5 − 2 design is 1/4 of a two-level, five-factor factorial design. Rather than the 32 runs that would be required for the full 2 5 factorial experiment, this experiment requires only ...
In the analytic theory of continued fractions, Euler's continued fraction formula is an identity connecting a certain very general infinite series with an infinite continued fraction. First published in 1748, it was at first regarded as a simple identity connecting a finite sum with a finite continued fraction in such a way that the extension ...
Order of operations. In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression . These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and ...
An example is 1*2 −3 2. The 1* denotes the only 1-vertex basic polyhedron. The 2 −3 2 is a sequence describing the continued fraction associated to a rational tangle. One inserts this tangle at the vertex of the basic polyhedron 1*. A more complicated example is 8*3.1.2 0.1.1.1.1.1 Here again 8* refers to a basic polyhedron with 8 vertices.
A number-line visualization of the algebraic addition 2 + 4 = 6. A "jump" that has a distance of 2 followed by another that is long as 4, is the same as a translation by 6. A number-line visualization of the unary addition 2 + 4 = 6. A translation by 4 is equivalent to four translations by 1.
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