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.
-Conrad
On 7/27/07, johnps11@bigpond.com johnps11@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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