Calculate the Unit Fraction Sum

Calculator for the unit fraction sum, or Egyptian fraction, of a common or decimal fraction. A common fraction is something like 3/4, the according decimal fraction is 0.75. A unit fraction has the form 1/n, whereas n is a natural number. The unit fraction sum gives the fraction as a sum of different unit fractions (and a natural number, if the fraction is larger than 1). A unit fraction sum is only possible for positive values. Please enter numerator and denominator of a common fraction or the value of a decimal fraction and press the according button.

Examples:
• the ordinary fraction 5/19 has the unit fraction sum 1/4 + 1/76
• the decimal fraction 0.024 has the unit fraction sum 1/42 + 1/5250. Here the calculation takes quite a while. The specified 5 seconds are probably not enough, depending on the speed of the computer used.

The calculation is really very computationally intensive, it can take a while and does not always produce the shortest possible unit fraction expansion. The algorithm used here starts with the largest possible unit fraction, this is the one with the smallest denominator. However, there may be shorter unit fractions with different starting points.
For too complicated fractions, such as 3/7 or 13/287, unfortunately, no result will be obtained. The calculation will be aborted after the specified number of seconds, and the unit fractions calculated up to that point will be displayed. Other fractions, such as the 0.024 mentioned above, will likely take longer than the default 5 seconds.

Unit fractions are the reciprocals of natural numbers. They can be more intuitive than ordinary fractions and play a role in some specific mathematical and physical calculations.