Did you know that fractions as we use them today didn't exist in
Europe until the 17th century? In fact, at first, fractions weren't
even thought of as numbers in their own right at all, just a way of
comparing whole numbers with each other. Who first used fractions?
Were they always written in the same way? How did fractions reach
us here? These are the sorts of questions which we are going to
answer for you. Read on ...
The word fraction actually comes from the Latin "fractio" which
means to break. To understand how fractions have developed into the
form we recognise, we'll have to step back even further in time to
discover what the first number systems were like.
From as early as 1800 BC, the Egyptians were writing fractions.
Their number system was a base 10 idea (a little bit like ours now)
so they had separate symbols for 1, 10, 100, 1000, 10 000, 100 000
and 1 000 000. The ancient Egyptian writing system was all in
pictures which were called hieroglyphs and in the same way, they
had pictures for the numbers:
Here is an example of how the numbers were made up:
Could you write down 3 581 in hieroglyphics?
The Egyptians wrote all their fractions using what we call unit
fractions. A unit fraction has 1 as its numerator (top number).
They put a mouth picture (which meant part) above a number to make
it into a unit fraction. For example:
Here is one fifth.
Can you work out how to write one sixteenth?
They expressed other fractions as the sum of unit fractions, but
they weren't allowed to repeat a unit fraction in this addition.
For example this is fine:
But this is not:
The huge disadvantage of the Egyptian system for representing
fractions is that it is very difficult to do any calculations. To
try to overcome this, the Egyptians made lots of tables so they
could look up answers to problems.
In Ancient Rome, fractions were only written using words to
describe part of the whole. They were based on the unit of weight
which was called the as. One "as" was made up of 12 uncia so
fractions were centred on twelfths. For example:
As with the Egyptian system, the words made it very difficult to do
calculations.
The Babylonians were the first people to come up with a more
sensible way of representing fractions. In fact they did this
before the Romans' methods but there was no contact between the two
civilisations. The Babylonians lived in the country we now call
Iraq in the Middle East. Their number system was organised around
the number 60, so we say it is base 60. In other words they grouped
numbers into 60s, whereas we group into 10s. (We still use base 60
in our measurement of time and angles.) However, they also grouped
into 10s and so only had two symbols, one for a unit and one for a
10:
Here are the numbers from 1 to 20.
Can you see the symbol for 1?
What about the symbol for 10?
How would you write 47?
The Babylonians simply extended their numbers to include fractions
in sixtieths, as we do for tenths, hundredths etc. However, they
didn't have a zero or anything like a decimal point. This made
reading numbers very confusing as they could be interpreted in
different ways. Here's an example:
From the table above, you can see that the two numbers are 12
and 15. Now, this is where it becomes confusing. This could mean
several different things:
| x60 |
Units |
Sixtieths |
Number |
|
12 |
15 |
|
| 12 |
15 |
|
720 + 15 |
So, although the Babylonians had a very sophisticated way of
writing fractions, it did have its drawbacks. Around 311BC they
devised a zero so this made things easier, but without a decimal
point, it was still difficult to distinguish fractions from whole
numbers.
We are now reaching the end of our journey through the history of
fractions! The format we know today comes directly from the work of
the Indian civilisation. The success of their way of writing
fractions is due to the number system they created which has three
main ideas:
i) Each figure has a symbol which isn't like the value it
represents
ii) The value of the figure depends on the position of it within
the entire number
iii) A zero is needed to mean nothing and also to fill the place of
units that are missing
By about 500AD, the Indians had developed a system from a way of
writing called brahmi , which had nine symbols and a zero. Again,
this was devised a long time before some of the other ways of
counting we have already discussed. However it was only through the
trading of the Arabs that these Indian numerals were spread to
Arabia where they were used in the same form. The chart below shows
how these brahmi symbols became the numbers we know today:
In India fractions were written very much like we do now, with one
number (the numerator) above another (the denominator), but without
a line. For example:
It was the Arabs who added the line (sometimes drawn
horizontally, sometimes on a slant) which we now use to separate
the numerator and denominator:
So here we have the fraction as we now recognise it. It is amazing
to think how much thought has gone into the way we write it down,
isn't it? Perhaps next time you use fractions, you'll remember
this.
All images reproduced by kind permission from http://www-groups.dcs.st-and.ac.uk
.
If you'd like to know more, check out these websites:
http://www-netra.ics.uci.edu/~eppstein/numth/egypt/
http://www-groups.dcs.st-and.ac.uk
http://www.math.buffalo.edu/mad/Ancient-Africa/
members.aol.com/jeff570/
http://www.gosai.com
"The Universal History of Numbers" by Georges Ifrah, published by
Harvill, is also a fantastic source of information.
Perhaps you could find out about other civilisation's number
systems.For information on the Greeks try:
http://www.math.tamu.edu/~dallen/history/gr_count/gr_count.html
And for Chinese numerals look at:
http://www.saxakali.com/color_asp/chinamh1.htm
The Mayan number system is also interesting:
http://www.saxakali.com/historymam2.htm
