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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 ...
A continued fraction in canonical form is an expression of the form ... 4 / 5 5 / 6 11 / 13 ... The simplest examples are the golden ratio φ = [1
When the golden ratio is used as the base of a numeral system (see golden ratio base, sometimes dubbed phinary or -nary), quadratic integers in the ring [] – that is, numbers of the form + for and in – have terminating representations, but rational fractions have non-terminating representations.
A simple fraction (also known as a common fraction or vulgar fraction) [n 1] 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 .
A continued fraction is an expression of the form = + + + + + where the a n (n > 0) are the partial numerators, the b n are the partial denominators, and the leading term b 0 is called the integer part of the continued fraction.
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, and recurrence relations.
If the pattern contains fractions, e.g. <4.5 3 3 | 3 4 3.5> the juggler after the bar is supposed to be half a count later, and all fractions are passes. social siteswap If both juggle the same pattern (although shifted in time), the pattern is called a social siteswap and only half of the pattern needs to be written: <4p 3| 3 4p> becomes 4p 3 ...
2.1 Reducing fractions. 2.2 ... etc. [3] [4] [5 ... may be defined alternatively and equivalently as the smallest positive integer d which can be written in the form ...