1fraction

1fraction is not a single, universally defined term in mathematics or computer science. In many contexts it is used informally to refer to unit fractions—the family of fractions with numerator 1, written in the form 1/n where n is a positive integer. Unit fractions appear in various areas of number theory and the history of mathematics, notably in the study of Egyptian fractions.

Unit fractions are the reciprocals of positive integers. They are rational numbers and form a subset of fractions. They can be added by finding a common denominator, and many rational numbers can be expressed as sums of unit fractions, a representation known as Egyptian fractions. For example, 3/4 = 1/2 + 1/4. Every positive rational number can be expressed as a sum of unit fractions in a finite or infinite process; the greedy algorithm (Egyptian fraction expansion) produces such representations for any positive rational number. The sequence of unit fractions 1, 1/2, 1/3, 1/4, ... relates to convergence properties, and the harmonic series sum_{n=1}^\infty 1/n diverges.

In computing or product naming, the term 1fraction may be used as a brand or label for software dealing with fractions or fixed-point arithmetic. Because there is no single standard definition, references to 1fraction should be interpreted according to the surrounding context.

See also: unit fraction; Egyptian fraction; rational number; fraction.