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Is a common fraction what we call an improper fraction


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Hi

 

Too lazy to research this.  Alcamus just said to express the answer as a common fraction x pi.  I put 10 1/2 pi and it marked me as incorrect as they wanted 21/2 pi.  I am used to converting to a proper fraction and/or simplifying so I just assumed a common fraction was that.  I am now guessing it isn't?

Edited by kiwik
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Weird I am pretty sure I had to even at university.  But maybe I am recalling wrong -  it is quite possible we converted the answers to decimals.  We were instructed to always to our calculations in fractions because it was more accurate to use 2/3 than a repeating decimal but obviously you don't express results fractions very often using the metric measurements.  Thanks I will just use improper fractions (which to me seem only partially simplified) and see how I go. Maybe I just read it wrong a bit too rather than it being an error.

 

ETA. On the plus side both times I made this kind of mistake I did in fact get the right answer.

Edited by kiwik
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A common fraction is a fraction where both numerator and denominator are integers.

I would recommend never to write things like 10 1/2* pi because that makes it unclear what exactly is multiplied with pi, unless you use parentheses. 

Edited by regentrude
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You almost never use mixed numbers beyond elementary school. They are too hard to work with. Middle school and up, just leave everything as a fraction, no matter whether the top or bottom number is the bigger one. By the time you get to algebra fractions, you will often not know which is bigger anyway...

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They may be using the Mathcounts definition of a common fraction:

 

A "common fraction" is to be considered a fraction in the form +/- a/b, where a and b are natural numbers and gcf(a,b) =1.  

 

A simplified "mixed number" is to be considered a fraction in the form +/- N a/b, where N, a, and b are natural numbers, a<b, and gcf(a,b) = 1.  

 

It's described on page 47 of the MathCounts handbook.  

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Thanks all.  I have done maths to second year university in NZ but I have been thinking and because of the odd way I did my highschool maths I think I didn't do much advanced algebra and no geometry past what was in general maths.  Somewhere I got it into my head that although it was OK to use a number like 20/6 in calculations it had to be converted to 3 1/3 for the answer.  I also hadn't heard "common fraction" before (or if I did it was over 20 years ago) so I guessed what it was and got it wrong (and I think it is the mathcounts definition).  I get the thing about parenthesis though. As soon as I have NZ$100 I am going to buy the text book and solution.

 

Thanks again.

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