The Joy of FractionsDate: 05/18/2002 at 17:23:36 From: Nicole Subject: fractions How come fractions are called fractions? How come they can be translated into decimals? Why do they hurt your brain when you first learn them? Date: 05/18/2002 at 18:45:55 From: Doctor Sarah Subject: Re: fractions Hi Nicole - thanks for writing to Dr. Math. According to Steven Schwartzman's book, _The Words of Mathematics, An Etymological Dictionary of Mathematical Terms Used in English_: The word 'fraction' comes from Latin 'fractus' which is the past participle of 'frangere' which means "to break." A fraction is literally a piece broken off something. In 16th-century English mathematics books, fractions were sometimes referred to as "broken numbers." For conversions, see the Dr. Math FAQ: Fractions, Decimals, Percentages http://mathforum.org/dr.math/faq/faq.fractions.html - Doctor Sarah, The Math Forum http://mathforum.org/dr.math/ Date: 05/18/2002 at 18:49:29 From: Doctor Ian Subject: Re: fractions Hi Nicole, The word 'fracture' means to break into pieces, and 'fraction' comes from the same root. When you break something into pieces, each piece is a 'fraction' of the whole. The reason a fraction can be translated into a decimal is that a fraction is really just a division that you haven't done yet. So when you see something like 3/4, it's just a way of saying "the number that you'd get when you divide 3 by 4". That is, 3/4 is just another name for 0.75, which is just another name for 75/100, and so on. Why would you want to have such a notation? Well, in many cases it turns out that you would divide by something now only to end up multiplying by by the same thing later. By putting off doing the multiplications and divisions, you can sometimes avoid doing them. (This is one of the few times in life that procrastination can actually pay off.) For example, you might end up translating a story problem into an equation like 3 6 12 5 11 - * - * -- * - * -- = ? 5 9 11 2 3 Now, you could go ahead and multiply all the terms in the numerator and denominator to get 3 6 12 5 11 11880 - * - * -- * - * -- = ----- 5 9 11 2 3 2970 and then you could divide those to get 4! But that's a lot of work, even with a calculator. It would be much easier to just rearrange the terms so that you can see which ones cancel each other out: \ \ \ 3 6 12 5 11 3 * 5 * 6 * 11 * 12 - * - * -- * - * -- = ---------------------- 5 9 11 2 3 2 * 3 * 5 * 9 * 11 \ \ \ 6 * 12 = ------ 2 * 9 And by breaking the remaining terms into factors, we can do the same kind of thing again: \ \ \ 2 * 3 * 3 * 4 = ------------- 2 * 3 * 3 \ \ \ = 4 So this is one of the things that makes fractions really useful! As for making your brain hurt, maybe you can learn to think of that feeling the way that body builders learn to think of muscle soreness: as a sign of growth. When a body builder lifts a lot of weights, his muscles hurt the next day, but that's partly because they're growing, so the next time he tries to lift the same weights, it will be easier. Maybe it's the same thing with brains? I hope this helps. Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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