Why Were Fractions Invented?Date: 11/26/2007 at 23:16:10 From: Dominique Subject: Fractions Why were fractions invented? Date: 11/27/2007 at 09:20:28 From: Doctor Peterson Subject: Re: Fractions Hi, Dominique. Fractions were invented to provide a way to work with quantities smaller than one, such as 2/3 (or quantities between two other whole numbers, such as 3 2/3). If we had only whole numbers, then the only way to talk about such quantities would be to use a smaller unit. In fact, that's essentially what the Romans did (who weren't very good mathematicians in general). They could talk only about whole numbers of feet; when they wanted to work with parts of feet, they would change to inches (of which there were, and are, 12 in each foot). Then what we might call 1/12 foot would be called 1 inch, using a whole number; 1/4 foot would be called 3 inches. (Our word "inch" comes from their word "uncia", which meant 1/12 of anything--the smaller unit). But what if your measurement isn't even a whole number of inches? Then you'd need a still smaller unit to measure it. If you want to be very precise, things get more and more complicated. Fractions are sort of do-it-yourself units. You decide what size unit you need in order to measure something, by choosing how many of them there will be in each of the existing unit; say you want 8 units per foot. Then the new unit is called an eighth, and rather than writing its name we just call it 1/8. Now we can measure any number of eighths; 3 of them is written as 3/8. The numerator tells how many of the unit you have, and the denominator tells what the unit is. (The word "numerator" is Latin for "numberer"--how many; the word "denominator" is Latin for "namer"--what kind of unit.) This makes it possible to measure all sorts of things without having to name lots of new units. Moreover, by having a nice way to write them, we can add, subtract, multiply, and divide any fractions easily (compared to what the Romans would have had to do, if they even bothered to try). And that's the benefit of fractions. This kind of fraction was invented hundreds of years after the end of the Roman empire, by Hindu mathematicians, and our notation (using the fraction bar) was established by Arabic mathematicians. There are other solutions to the same problem. The decimals we use (which you may or may not have learned about yet) were invented by the Arabs, and got their current form around 1500 in Europe. But the ancient Babylonians had a very similar idea, based on 60 rather than 10, which was used by ancient astronomers--and is still the basis of our degree measurement of angles, as well as minutes and seconds of time. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/