There is nothing wrong with vulgar fractions, except maybe the name puts
people off.
In terms of dividing something into equal parts, the 1 over the number
of parts type of vulgar fraction, e.g. 1/4 or 1/9, is very useful, such
as dividing a cake into 4 or 9 equal parts.
But when it comes to measuring things, imperial tended to use vulgar
fractions for things smaller than an inch as it never had a unit smaller
than 1 inch. And without the great accuracy being available that we have
today, people just divided things into halves, quarters, eighths.
But with metric, and decimal-based measurement, there is no need for
vulgar fractions, at least if accuracy is needed. But there is nothing
wrong with talking of half a kilometre, a third of a litre, etc. Drinks
cans in the UK are often sold with a measure of 330 ml, which could be
(approximately) described as 1/3 of a litre.
Nothing wrong with vulgar fractions, but sometimes they are just not
necessary, and sometimes they are very useful. It is when we see silly
things like 193/256 that it becomes silly. Things like 3/4 are very
useful, but that can also be quickly seen as 75% or 0.75, whereas
193/256 is very hard to visualise.
David King
Buy UKMA's report "A Very British Mess" ISBN 0750310146
http://www.ukma.org.uk/Docs/pubs.htm
Avoid confusion with conversion, just learn to think metric!
http://www.thinkmetric.org.uk
Stephen Humphreys wrote:
Fractions have to be taught as they are commonly used in day to day
life (in a less than mathematical way).
The old "pizza argument" could be used - ie to visualise cutting it up
in to quarters or eighths. One can't expect a kid to only recognise a
pizza cut into 10 pieces to make sense of the words that describe what
that looks like.
Plus manipulation of fractional arithmentic taxes the mind in a
healthy way as part of education.
Incidentally - My weakest skill at school was fractions - I would have
LOVED for them not to be taught when I was at school ;-)
From: "Philip S Hall" <[EMAIL PROTECTED]>
Reply-To: [EMAIL PROTECTED]
To: "U.S. Metric Association" <[email protected]>
Subject: [USMA:34807] Re: fractions
Date: Tue, 11 Oct 2005 19:50:39 +0100
Without rounding, 1/3 becomes 0.3333333333333 and 1/7 becomes
0.142857142.
What's wrong with 0.33 or 33% or 0.14? Accurate enough for most
people's needs.
I don't think we're on the same wavelength here or maybe we're at
cross purposes.
I'm perfectly happy with the idea that decimal form is better for
measurment. With decimal we can round measurements or express them to
any degree of accuracy we like with an appropriate choice for the
number of significat digits and the last digt for rounding. That
reflects the nature of measurement itself. All measurements are an
approximation to varying degrees. Decimal notation lends itself to
that perfectly.
What concerns me is the suggestion that somehow fractions (of the
form x/y) can be surgically removed from the mathematics curriculum.
I don't understand how you can talk about tenths and hundredths etc,
in isolation from the general concept of an nth of something! For
example 0.237 is just code for 237/1000 They are closely related and
inseparable.
Now I realise that some of you are merely saying that it is a waste
of time learning to do arithmetic with x/y type fractions because
nobody uses them in practice, except maybe to cope with measurement
units where you end up with awkward fractions.
Well I think there is more to it than that. Even without non-decimal
measurement systems it would still be quite important for kids to
learn the principles. But in order to teach it you need a means of
assessment. That can only be done by exercises that will inevitably
involve a certain amount of doing arithmetic.
There is also the point that time isn't decimal nor is angular
measurement in degrees.
It's all too easy for the likes of us as adults who take for granted
what we know about fractions and are able to instincitively apply
them to the idea of a half or a quarter or a two thirds of something.
We are able to do this because we have benefitted from a rounded
education in basic mathematics. We musn't try to deprive future
generations of this. It's not part of the deal where metrication is
concerned.
Phil Hall
