The Secret of Egyptian Fractions

Photo from Library of Congress via pingnews.

Archaeology professor Dr. Fibonacci Jones came home from a long day of lecturing and office work. Stepping inside the front door, he held up a shiny silver disk.

“Ta-da!” he said.

Rhind papyrus

“All right!” said his daughter Alexandria. “The photos are here.”

They had to chase Alex’s brother Leon off the computer so they could view the images on the CD, but that wasn’t hard. He wanted to see the artifacts, too. Alex recognized several of the items they had dug up from the Egyptian scribe’s burial plot: the wooden palette, some clay pots, and of course the embalmed body.

Then came several close-up pictures of writing on papyrus.

Photo from

How to Write Egyptian Fractions

“I remember how to read the Egyptian numbers,” Alex said, “but what are these marks above them?”

Dr. Jones nodded. “I thought you would catch that. Those are fractions. The scribe places an open mouth, which is the hieroglyph ‘r’, over a number to make its reciprocal.”

“I know that word,” Leon said. “It means one over the number. Like, the reciprocal of 12 is 1/12, right?”

“That is right. 1/12 would be written as…”

The Rest of the Story

As I transcribed this article from my old math newsletter, I realized that it would require more graphics than I was willing to construct. LaTex does not handle Egyptian hieroglyphs — or at least, I don’t know how to make it do so. Instead, I decided to scan the newsletter pages and give them to you as a pdf file:

Right-click and choose “Save” to download:

The file includes a student worksheet for Egyptian fractions from 1/2 to 9/10.

Egyptian Fractions: The Answer Sheet

The answers are now posted.

To Be Continued…

Read all the posts from the January/February 1999 issue of my Mathematical Adventures of Alexandria Jones newsletter.

10 thoughts on “The Secret of Egyptian Fractions

  1. How funny, I was just wondering today whether Roman Numerals had any way to write factions. (In particular, my kids were wondering how to write pi in Roman Numerals, the answer to which I’m sure is “you don’t”…)

  2. Pi in Roman numerals? Oh, my!

    I haven’t read much about Roman use of fractions. I did read a section of Augustine’s City of God where he shows the influence of Egyptian-style fractions on Roman thinking. He talks about 6 being a perfect number, and he uses unit fractions (which he calls aliquot parts) to name the factors:

    These works are recorded to have been completed in six days, …because six is a perfect number—not because God required a protracted time, …but because the perfection of the works was signified by the number six. For the number six is the first which is made up of its own parts, i.e., of its sixth, third, and half, which are respectively one, two, and three, and which make a total of six.

    In this way of looking at a number, those are said to be its parts which exactly divide it, as a half, a third, a fourth, or a fraction with any denominator…four is a part of nine, but not therefore an aliquot part; but one is, for it is the ninth part; and three is, for it is the third. Yet these two parts, the ninth and the third, or one and three, are far from making its whole sum of nine.

    …Of the number twelve, again, the parts added together exceed the whole; for it has a twelfth, that is, one; a sixth, or two; a fourth, which is three; a third, which is four; and a half, which is six. But one, two, three, four, and six make up, not twelve, but more, viz., sixteen.

    So much I have thought fit to state for the sake of illustrating the perfection of the number six, which is, as I said, the first which is exactly made up of its own parts added together; and in this number of days God finished His work. And, therefore, we must not despise the science of numbers….

  3. I think my youngest had in mind something like:


    but of course it doesn’t make sense to use roman numerals in that way (a non-base-10 representation for decimal notation…)

    Interesting quote about the aliquot parts…

  4. Hey, I noticed that entry about Egyptian Fractians. When I learned how to subtract, I learned the Egyptian way….no regrouping….

  5. This is really cool. I am currently doing an English teaching course and hoping to go to China at some point and we recently covred Roman numerals. What a headache! lol.

    The PDF was rather helpful. Maybe this will come of some use to some students I provide this too, but obviously this will have to be Student Friendly to my Chinese students 🙂

    Thanks for this Deinise!

    Holly X

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