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In general, a common fraction is said to be a proper fraction, if the absolute value of the fraction is strictly less than one—that is, if the fraction is greater than −1 and less than 1. [14] [15] It is said to be an improper fraction, or sometimes top-heavy fraction, [16] if the absolute value of the fraction is greater than or equal to 1 ...
Slices of approximately 1/8 of a pizza. A unit fraction is a positive fraction with one as its numerator, 1/ n. ... greater than one, or less than one respectively. ...
The greedy algorithm for Egyptian fractions finds a solution in three or fewer terms whenever is not 1 or 17 mod 24, and the 17 mod 24 case is covered by the 2 mod 3 relation, so the only values of for which these two methods do not find expansions in three or fewer terms are those congruent to 1 mod 24. [12]
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 ...
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.
Fibonacci applies the algebraic identity above to each these two parts, producing the expansion 8 / 11 = 1 / 2 + 1 / 22 + 1 / 6 + 1 / 66 . Fibonacci describes similar methods for denominators that are two or three less than a number with many factors.
For instance, the golden ratio = (+) / = is a reduced surd because it is greater than one and its conjugate () / = is greater than −1 and less than zero. On the other hand, the square root of two 2 = ( 0 + 8 ) / 2 {\displaystyle {\sqrt {2}}=(0+{\sqrt {8}})/2} is greater than one but is not a reduced surd because its conjugate − 2 = ( 0 − ...
Without computing a common denominator, it is not obvious as to what + equals, or whether is greater than or less than . Any common denominator will do, but usually the lowest common denominator is desirable because it makes the rest of the calculation as simple as possible.