# [Newbies] Proper fractions?

Sat Jul 28 00:37:06 UTC 2007

```Hi, I agree with you 100% in this regard because I have arrived at the
same conclusion.  Thus, a better way to extend the image to support
mixed-numbers would be to create a class called MixedFraction which is
subclassed from Fraction.

On 7/27/07, johnps11 at bigpond.com <johnps11 at bigpond.com> wrote:
> > Hey, guys:
> >
> >       (And who came up with that whole "improper" terminology? Some guys with
> > small numerators, I'd bet....)
> >
> >       ===Blake===
>
> I spent many years teaching remedial maths.  The whole
> proper/improper/mixed number concept messes with many kids learning
> arithmetic with fractions.
>
> As I recall,  proper fractions used to be written as a sum of partial
> fractions with numerator 1. For example:
>
> 3/8 = 1/4 + 1/8 so it was written as a proper fraction as
>
> 1  1
> -  -
> 4  8
>
> 2/5 = 1/4 + 1/10 + 1/20
>
> 1  1  1
> -  -  -
> 4  10 20
>
> 12/7 = 1 + 1/2 + 1/3 + 1/42
>
>   1  1  1
> 1 -  -  -  (a mixed number)
>   2  3  42
>
> If it was clear from context that a fraction was being discussed it would
> be written just by listing the denominators:
>
> 1 2 3 42
>
> This caused much confusion, is 2 4  3/4 or 9/4 (i.e. a mixed number or a
> proper fraction)?
>
> 2 2 4 was always 11/4 though (as the second 2 had to denote 1/2).
>
> A fraction written any other way (excepting continued fractions) was
> considered 'improper'.
>
> Later usage allowed for larger numerators.  Improper fractions were then
> fractions where the numerator was larger than the denominator, as we use
> today.  Proper fractions are always < 1.
>
> 1 3/4 as meaning 7/4 is called a mixed number, and use of mixed numbers is
> a cause for many errors,  as if written messily it can easily be read as
> 13/4 or even 1/14.
>
> To my mind a class that displays as a mixed number should be a subclass of
> Fraction, as the default of displaying a fraction as an improper fraction
> has no room for ambiguity.
>
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```