Estimating FractionsDate: 12/02/2001 at 17:36:41 From: Justin Subject: Estimating Fractions Dr. Math, I am completely clueless about the process of estimating fractions. Here is a simple example of an estimation question using fractions: There is a plate of assorted cookies. 1/6 of these cookies are chocolate chip, while 1/5 of them are peanut butter. The rest of the cookies on the plate are regular. What fraction do the regular cookies make? Sincerely, Justin Date: 12/03/2001 at 15:31:50 From: Doctor Ian Subject: Re: Estimating Fractions Hi Justin, In this case, I think what you're supposed to recognize is that 1/5 and 1/6 are very close to the same fraction, with 1/5 being a little larger. So one way you might proceed would be to say that 1/5 + 1/6 ~ 1/5 + 1/5 = 2/5 which would leave 3/5 of the cookies as regular. (The '~' is pronounced 'approximately equals'. It's this kind of approximation that you're doing when you estimate something.) On the other hand, you might say that 1/5 + 1/6 ~ 1/6 + 1/6 = 2/6 = 1/3 which would leave 2/3 of the cookies as regular. So you could say that 'between 1/3 and 2/5 of the cookies are regular'. The idea is that this is much easier (and often much neater) than finding the _actual_ answer: 1/5 + 1/6 = 6/30 + 5/30 = 11/30 Yuck! Note that 1/3 = 0.3333... 11/30 = 0.3666... 2/5 = 0.40 so the real answer is in between the two estimates... which is exactly what you'd expect if you made one estimate too large and the other too small. The basic idea with estimation is always the same: you agree to accept a little less accuracy in exchange for doing a lot less work. Sometimes that's a good trade, and sometimes it's not. Part of learning to estimate things is learning when estimation is a good idea, and when it's a bad idea. I hope this helps. Write back if you'd like to talk more about this, or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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