Egyptian Fraction Calculator

How to use the Egyptian Fraction Calculator

1. 1Enter a numerator and a denominator.
2. 2Pick the units or options from the menus if the Egyptian fraction tool offers them.
3. 3Read the Egyptian fraction in the large result box.
4. 4Look at the extra rows for related figures.
5. 5Press Copy result to keep the answer.

When you need the Egyptian fraction

People use Egyptian fractions in number theory puzzles, history lessons and to share things fairly: dividing 4 loaves among 13 people by cutting each loaf into quarters and smaller parts.

The greedy method always finishes, but it can produce very large denominators, and it is not always the shortest answer. For 5/121 it gives a denominator with many digits, while other methods find shorter sums.

How the Egyptian fraction is worked out

At each step take the largest unit fraction 1/d that is not bigger than what is left, where d is the denominator divided by the numerator, rounded up. Subtract it and repeat until nothing is left. 4/13: the largest unit fraction below it is 1/4, leaving 3/52. Next is 1/18, leaving 1/468. So 4/13 = 1/4 + 1/18 + 1/468.

Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.

• Reduces the fraction first
• Exact whole-number arithmetic
• Shows the number of terms

Mistakes to avoid with Egyptian fraction

Do not expect repeated terms: a valid Egyptian fraction uses each unit fraction at most once. Improper fractions such as 7/4 are split into the whole part plus a fraction, so enter a fraction below 1 for the classic result.

On phone and computer

On a phone, type into the boxes one after another and read the Egyptian fraction underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the Egyptian fraction move. The egyptian fraction calculator works the same on both.

Checking your Egyptian fraction by hand

A good habit is to test the egyptian fraction calculator with a case you already know. 4/13: the largest unit fraction below it is 1/4, leaving 3/52. Next is 1/18, leaving 1/468. So 4/13 = 1/4 + 1/18 + 1/468.

If your own figures give a surprising answer, repeat the working yourself: At each step take the largest unit fraction 1/d that is not bigger than what is left, where d is the denominator divided by the numerator, rounded up. Subtract it and repeat until nothing is left. Small differences usually come from rounding, from mixing units, or from a typing slip in one of the inputs. Unit fractions are a nice puzzle, and these tools help when you want more. Use the Fraction Calculator to check that the parts add up, see another way to write numbers with the Continued Fraction Calculator, and count combinations with the Factorial Calculator.

Features

• Each unit fraction is used once
• Greedy denominators can be huge
• Not always the shortest sum
• Clear messages when the Egyptian fraction inputs make no sense
• Copy the result with one tap
• Private: nothing is uploaded

Frequently asked questions