How this calculation works
The first unit fraction is the largest one that fits inside the remainder. Other sums may represent the same fraction.
THE FORMULA
Repeatedly subtract 1/ceil(b/a) from the remaining fraction a/bA worked example
4/13 becomes 1/4, then 1/18, then 1/468.
Good to know
Use a proper fraction. The greedy sum can have large denominators.
Reference: OpenStax Prealgebra (opens in a new tab) ↗
Read the result
Apply the greedy algorithm to express a positive proper fraction as a sum of distinct unit fractions.
The primary result is labeled “Unit-fraction sum”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Use a proper fraction. The greedy sum can have large denominators.
For a related exercise, try the fraction calculator.
A few questions, answered
How can I check the default inputs by hand?
4/13 becomes 1/4, then 1/18, then 1/468.
Which rule does this calculator apply?
Repeatedly subtract 1/ceil(b/a) from the remaining fraction a/b