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### History of Fractions

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Date: 12/7/95 at 9:30:11
From: Anonymous
Subject: History of Fractions

I have several math classes coming to our school media center next
week to research the history of fractions.  The problem is, our media
center does not have the right resources to help students with their
assignment.

They are trying to find out how fractions developed and how they
have been used in history.

For example, how did the Babylonians, Ancient Chinese, Egyptians,
Greeks, or Hindus use fractions?  How were fractions written?  Which
operations (addition, subtraction, multiplication, division), if any,
could be carried out with fractions?  How did they expand the use of
fractions?

We have a few books that cover what the numerals of these societies
looked like, but nothing about the history of fractions in ancient
cultures.  Our public library and our district high school library
didn't have anything either.

```

```
Date: 3/8/96 at 23:45:47
From: Doctor Jodi
Subject: Re: History of Fractions

Hi there!  If you have access to a web browser, you'll find a detailed
description of the Babylonian and Egyptian mathematical system,
including some discussion of fractions, at

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_and_Egyptian.html

Briefly, the Babylonians used base 60, rather than base 10.  Their
fractional system survives in the hours minutes and seconds notation we
still use.

The Chinese system is described at

http://aleph0.clarku.edu:80/~djoyce/mathhist/china.html

Briefly, the Chinese used a symbol for the numbers 1-10, 100, 1000, and
10000.  2034 would be written 2, 1000, 3, 10, 4 (2 * 1000 + 3*10 +4)

Small bamboo counting rods were used for calculations.  Positions from
left to right gave place value. Fractions, as far as I can tell from
this description, were like ours.  You might find a better description
in the original sources, Development of Mathematics in China and Japan
(Mikami) and Chinese Mathematics, A Concise History (Li Yan and
DuShiran).

Some of the resources from the bibliography at

http://aleph0.clarku.edu:80/~djoyce/mathhist/numerals.html

may also be useful.

From my understanding of Greek mathematical history, I gather that
Greeks emphasized the use of ratios.  Euclid's ELEMENTS contains a book
just on ratios and several others which depend heavily upon it.  You may
be particularly interested in exploring the golden ratio.

I hope this will give you the information you're looking for.  If you'd
us again.

-Doctor Jodi,  The Math Forum

```
Associated Topics:
Middle School History/Biography

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