Search results
Results from the WOW.Com Content Network
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.
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 ...
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 particular F n contains all of the members of F n−1 and also contains an additional fraction for each number that is less than n and coprime to n. Thus F 6 consists of F 5 together with the fractions 1 / 6 and 5 / 6 . The middle term of a Farey sequence F n is always 1 / 2 , for n > 1.
It is known [20] that every x / y with odd y has an expansion into distinct odd unit fractions, constructed using a different method than the greedy algorithm. It is possible to use brute-force search algorithms to find the Egyptian fraction representation of a given number with the fewest possible terms [ 21 ] or minimizing the largest ...
1. Means "greater than or equal to". That is, whatever A and B are, A ≥ B is equivalent to A > B or A = B. 2. Between two groups, may mean that the second one is a subgroup of the first one. 1. Means "much less than" and "much greater than".
On the other hand, the square root of two = (+) / is greater than one but is not a reduced surd because its conjugate = / is less than −1. Galois proved that the regular continued fraction which represents a quadratic surd ζ is purely periodic if and only if ζ is a reduced surd.
The repeating sequence of digits is called "repetend" which has a certain length greater than 0, also called "period". [5] In base 10, a fraction has a repeating decimal if and only if in lowest terms, its denominator has any prime factors besides 2 or 5, or in other words, cannot be expressed as 2 m 5 n, where m and n are non-negative integers.