The History of Fractions

In this article we will look into the history of the fractions, and we’ll find out what the heck that line in a fraction is called anyway.

Nearly everybody uses, or has used, fractions for some reason or another. But most people have no idea of the origin, and almost none of them have any idea what that line is even called. Most know ways to express verbally that it is present (e.g. “x over y-3,” or “x divided by y-3″), but frankly, it HAS to have a name. To figure out the name, we must also investigate the history of fractions.

The concept of fractions can be traced back to the Babylonians, who used a place-value, or positional, system to indicate fractions. On an ancient Babylonian tablet, the number, appears, which indicates the square root of two. The symbols are 1, 24, 51, and 10. Because the Babylonians used a base 60, or sexagesimal, system, this number is (1 * 60 0 ) + (24 * 60-1 ) + (51 * 60-2 ) + (10 * 60-3 ), or about 1.414222. A fairly complex figure for what is now indicated by √2.

In early Egyptian and Greek mathematics, unit fractions were generally the only ones present. This meant that the only numerator they could use was the number 1. The notation was a mark above or to the right of a number to indicate that it was the denominator of the number 1.

The Romans used a system of words indicating parts of a whole. A unit of weight in ancient Rome was the as, which was made of 12 uncias. It was from this that the Romans derived a fraction system based on the number 12. For example, 1/12 was uncia, and thus 11/12 was indicated by deunx (for de uncia) or 1/12 taken away. Other fractions were indicated as :

10/12 dextans (for de sextans),
3/12 quadrans (for quadran as)
9/12 dodrans (for de quadrans),
2/12 or 1/6 sextans (for sextan as)
8/12 bes (for bi as) also duae partes (2/3)
1/24 semuncia (for semi uncia)
7/12 septunx (for septem unciae)
1/48 sicilicus
6/12 or 1/2 semis (for semi as)
1/72 scriptulum
5/12 quincunx (for quinque unciae)
1/144 scripulum
4/12 or 1/3 triens (for trien as)
1/288 scrupulum

This system was quite cumbersome, yet effective in indicating fractions beyond mere unit fractions.

The Hindus are believed to be the first group to indicate fractions with numbers rather than words. Brahmagupta (c. 628) and Bhaskara (c. 1150) were early Hindu mathematicians who wrote fractions as we do today, but without the bar. They wrote one number above the other to indicate a fraction.

The next step in the evolution of fraction notation was the addition of the horizontal fraction bar. This is generally credited to the Arabs who used the Hindu notation, then improved on it by inserting this bar in between the numerator and denominator. It was at this point that it gained a name, vinculum. Later on, Fibonacci (c.1175-1250), the first European mathematician to use the fraction bar as it is used today, chose the Latin word virga for the bar.

The most recent addition to fraction notation, the diagonal fraction bar, was introduced in the 1700s. This was solely due to the fact that, typographically, the horizontal bar was difficult to use, being as it took three lines of text to be properly represented. This was a mess to deal with at a printing press, and so came, what was originally a short-hand, the diagonal fraction bar. The earliest known usage of a diagonal fraction bar occurs in a hand-written document. This document is Thomas Twining’s Ledger of 1718, where quantities of tea and coffee transactions are listed (e.g. 1/4 pound green tea). The earliest known printed instance of a diagonal fraction bar was in 1784, when a curved line resembling the sign of integration was used in the Gazetas de Mexico by Manuel Antonio Valdes.

When the diagonal fraction bar became popularly used, it was given two names : virgule, derived from Fibonacci’s virga; and solidus, which originated from the Roman gold coin of the same name (the ancestor of the shilling, of the French sol or sou, etc.). But these are not the only names for this diagonal fraction bar.

According to the Austin Public Library’s website, “The oblique stroke (/) is called a separatrix, slant, slash, solidus, virgule, shilling, or diagonal.” Thus, it has multiple names.

A related symbol, commonly used, but for the most part nameless to the general public, is the “division symbol,” or ÷ . This symbol is called an obelus. Though this symbol is generally not used in print or writing to indicate fractions, it is familiar to most people due to the use of it on calculators to indicate division and/or fractions.

Fractions are now commonly used in recipes, carpentry, clothing manufacture, and multiple other places, including mathematics study; and the notation is simple. Most people begin learning fractions as young as 1st or 2nd grade. The grand majority of them don’t even realize that fractions could have possibly been as complicated as they used to be, and thus, don’t really appreciate them for their current simplicity.

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33 Responses to “The History of Fractions”
  1. your mom Says...

    On October 6, 2008 at 5:47 pm

    it is very informal.


  2. Jena Dikes Says...

    On October 12, 2008 at 5:03 pm

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  4. ... Says...

    On October 12, 2008 at 8:19 pm


  5. Jenece Says...

    On October 20, 2008 at 6:34 pm

    I learn something I did not know about fraction thanks for the

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  6. fat kid Says...

    On October 21, 2008 at 10:37 pm

    HIS DOESNT HELP AT ALL!!!!!!!


  7. sexy mamma Says...

    On October 21, 2008 at 10:39 pm

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  8. James Says...

    On October 21, 2008 at 10:40 pm

    was this sopposed to help?


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  10. @:-} Says...

    On October 21, 2008 at 10:46 pm

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  11. Peep by student Says...

    On October 23, 2008 at 2:21 pm

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  14. jack Says...

    On November 17, 2008 at 10:43 pm

    this helped me allot with my report on fractions and i found it very informal. thank you


  15. phenushkka the polish leaf Says...

    On November 18, 2008 at 10:47 am

    i found it hard to concentrate and to read it because it looked sooooo boring. you should make it look more interesting and eye catching so i can bare it.


  16. Ivanushka Says...

    On November 26, 2008 at 3:10 am

    So interesting it made me understand fractions better.:)


  17. bob Says...

    On December 5, 2008 at 7:04 pm

    Are the people saying informal trying to say informational?


  18. student Says...

    On December 17, 2008 at 8:24 pm

    thanks for helping with my project


  19. cool_gal Says...

    On January 27, 2009 at 7:16 am

    this site helped me a lot…..thanks


  20. COOL SITE! Says...

    On February 11, 2009 at 5:21 am

    ok seriously it helped a lot like 75% of my work. It is informational and interesting. For you who did not understand should go to google and type history for kids. and do your dumb stuff there.
    thx


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    On February 18, 2009 at 8:36 am

    its bakvaas. it didn’t help me in my project.suggest that get some interesting facts about fractions. don’t bore us. totallyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy bakvas


  22. Rebecca Says...

    On March 6, 2009 at 8:35 pm

    I have to do research on the history of fractions to incorporate into a mini-math unit for a student teaching assignment and this was very helpful! Thanks :)


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  33. Thanxs Says...

    On March 19, 2011 at 9:23 pm

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