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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 ...
f-number. Diagram of decreasing apertures, that is, increasing f-numbers, in one-stop increments; each aperture has half the light-gathering area of the previous one. An f-number is a measure of the light-gathering ability of an optical system such as a camera lens. It is calculated by dividing the system's focal length by the diameter of the ...
The extremes of the meantone systems encountered in historical practice are the Pythagorean tuning, where the whole tone corresponds to 9:8, i.e. (3:2) 2 / 2 , the mean of the major third (3:2) 4 / 4 , and the fifth (3:2) is not tempered; and the 1 ⁄ 3-comma meantone, where the fifth is tempered to the extent that three ...
Unit fractions can also be expressed using negative exponents, as in 2 −1, which represents 1/2, and 2 −2, which represents 1/(2 2) or 1/4. A dyadic fraction is a common fraction in which the denominator is a power of two, e.g. 1 / 8 = 1 / 2 3 . In Unicode, precomposed fraction characters are in the Number Forms block.
Steep is above 9:12 (3 in 4) [4] (21:12) (7 in 4) and may require extra fasteners. US convention is to use whole numbers when even (e.g. "three in twelve") or the nearest single or two-digit fraction when not (e.g. either "five and a half in twelve" or "five point five in twelve", each expressed numerically as 5 + 1 ⁄ 2 :12 and 5.5:12 ...
Note value. In music notation, a note value indicates the relative duration of a note, using the texture or shape of the notehead, the presence or absence of a stem, and the presence or absence of flags/ beams /hooks/tails. Unmodified note values are fractional powers of two, for example one, one-half, one fourth, etc.
Being a highly composite number, when 120 was split into all these fractions, an integer was obtained in all cases except one – the points awarded for a draw in a 3-match series should be 13 1 ⁄ 3 (a third of a third of 120), but the 1 ⁄ 3 had been dropped.
The final result, 4 / 3 , is an irreducible fraction because 4 and 3 have no common factors other than 1. The original fraction could have also been reduced in a single step by using the greatest common divisor of 90 and 120, which is 30. As 120 ÷ 30 = 4, and 90 ÷ 30 = 3, one gets = Which method is faster "by hand" depends on the ...