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The entire fraction may be expressed as a single composition, in which case it is hyphenated, or as a number of fractions with a numerator of one, in which case they are not. (For example, "two-fifths" is the fraction 2 / 5 and "two fifths" is the same fraction understood as 2 instances of 1 / 5 .) Fractions should always be ...
Multiplication by one half is equivalent to division by two, or "halving"; conversely, division by one half is equivalent to multiplication by two, or "doubling". A square of side length one, here dissected into rectangles whose areas are successive powers of one half. A number raised to the power of one half is equal to its square root.
Simple fractions can sound more harmonious than complex fractions; for instance, an octave is a simple 2:1 ratio and a fifth is the relatively simple 3:2 ratio. The table below gives frequency ratios that are mathematically exact for just intonation , which meantone temperaments seek to approximate.
Two fractions a / b and c / d are equal or equivalent if and only if ad = bc.) 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 ...
However, if the fraction 1/1 is replaced by the fraction 2/2, which is an equivalent fraction denoting the same rational number 1, the mediant of the fractions 2/2 and 1/2 is 3/4. For a stronger connection to rational numbers the fractions may be required to be reduced to lowest terms, thereby selecting unique representatives from the ...
Ratio of a circle's circumference to its radius. Equal to ... Rational numbers have two continued fractions; the version in this list is the shorter one.
A similar scenario unfolded in 2004 with Apophis, an asteroid initially projected to have a 2.7 percent chance of striking Earth in 2029. Further observations ruled out an impact. "City killer ...
A rational number, which can be expressed as finite continued fraction in two ways, z = [a 0; a 1, ..., a k − 1, a k, 1] = [a 0; a 1, ..., a k − 1, a k + 1] = p k / q k will be one of the convergents for the continued fraction expansion of a number, if and only if the number is strictly between (see this proof)