# 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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I think it's probably an error, as I've never heard the term common fraction used like that. But for future reference, in advanced math you virtually never convert to a "proper fraction" and should leave things in simplified improper form.

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Weird I am pretty sure I had to even at university. &nbsp;But maybe I am recalling wrong - &nbsp;it is quite possible we converted the answers to decimals. &nbsp;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. &nbsp;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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10 and 1/2 would be a "mixed fraction"

21/2 "improper fraction"

Here's where I looked:

https://www.mathsisfun.com/definitions/mixed-fraction.html

(Because I wasn't quite sure I had the names right.) :hat:

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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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Common fraction is a FRACTION with the numerator and denominator as integers and it is simplified.  It could be 2/3 or it could be 21/5. A simplified improper fraction is also called a common fraction.

If you change 21/5 to 4 1/5 then it is a mixed number.

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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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Art Reed really helped us by stating that the word improper is so mis leading, and he calls them

algebraic Fractions meaning that for the rest of your life after pre algebra you never convert to a mixed number ...because they're too hard to work with in algebra!

I never heard the term common before though

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