History Of Fractions

 

The other day, in my trades math class, I was asked a question I couldn’t answer.  It wasn’t the usual “when will I use it?”, instead it was “Where did fractions come from?”.  My mind just blanked because I’d never thought about it.  As far as fractions go, they didn’t appear in Europe in the form we use until the 17th century but where did they come from?  How did they evolve?

The word fraction comes from the Latin word “fractio” meaning to break.  The Egyptians used their own version of fractions as early as 1800 BC.  Although Egyptians used their version of base 10, they had individual symbols for 10, 100, 1000, etc so when you did a number like 3250, you ended up using the symbol for 1000 three times, the symbol for 100 twice and five symbols for 10. 

Egyptians even had their own version of unit fractions where they had a numerator of 1 which was assumed because they used a mouth to indicate it was a fraction with the denominator illustrated below the mouth.  For instance, ⅕ had the mouth with five sticks below it. This meant they had to express fractions such as ¾ using two different fractions such as ½ + 1/4 .  However, they had a restriction where you couldn’t repeat a fraction.  So if you wanted to represent 2/7, you can’t use 1/7 + 1/7.

On the other hand, the Romans preferred using describing parts of a whole using words rather than symbols for fractions.  The system was based on 12 unica rather than base 10. Unfortunately using words only to describe the fraction made it hard to carry out calculations.  

The Babylonians had a base 60 number system so their fractions were based on sixteenths but they didn’t have a real way to distinguish fractions from regular numbers which made it more difficult to tell what was going on.  Eventually, they added a zero which helped a bit but it was India where fractions began appearing in a form closer to today’s form except they didn’t use that division line to separate the numerator from the denominator. The Arabs were the ones who added that part to make it much closer to what we know.

Along the way, the Chinese established many of the rules for calculating with fractions such as reducing fractions to simplest form and rules on adding, multiplying and dividing them while using a common denominator.  The Chinese didn’t use improper fractions, instead they relied on mixed numbers. In the mid 1500’s one mathematician published the first book relating fractions to their decimal equivalents.  

Now I know a bit more about the history of fractions and I can answer the question the next time it is asked.  Let me know what you think, I’d love to hear.  Have a great day.