Re: Explaining a common fraction

On Wed, 25 Jan 2006 15:45:33 -0400, "BarryAC"
<barrymalvina@xxxxxxxxxxxxx> wrote:

>Happy new year from Barbados! I've posted before, and you have been very
>helpful. I am really a science teacher, but I have a little job here
>teaching adults basic numeracy. So I said to them, as in most primary text
>books apparently, that the common fraction (eg 9/14) means 9 divided by 14
>and if you want to convert to decimals use the long division algorithm (or a
>calculator). But WHY does this work? I am looking for an explanation to
>assist understanding, and wonder how many primary teachers could provide
>this. Any suggestions please? Barry AC.

I'm not a primary teacher, but neither should they need, or be
expected to give such explanations to their young charges, so you
shouldn't necessarily ask that of them.

Why? You are changing the scale from the given denominator to a
multiple of 10. The reason for that is the reason for using the
decimal system ...It's generally easier to visualise, or conceptualise
those values, as it is to use percentages, and then convert back and
forth there as well.

In any division, you must decide at some point on the accuracy ...how
many figures. So, let's go for three decimal places [thousandths] for
sake of argument.

Now, 7/16 = x/1000. So x = 7000/16, and to find "x" you must do the
division to a whole value, which will then become the decimal part to
the required number of places. In this case 7000/16 = 438 [rounded
up], and the decimal equivalent is then 0.438.

So, again, what you have really found is that 7/16 = 438/1000
[approximately], and have been involved with a most fundamental of
concepts in the study of fractions ...equivalence... even if only
approximate in some instances.

That said, do not underestimate the difficulties met in the process of
long division by those who have trouble with it. A long time ago, I
taught myself programming, and in the process decided to do an
algorithm on string functions to find a division to any number of
decimal places. It was a learning experience to realise the minute
detail involved in the process. We seem to sort of flash through it,
but in reality we are going through those smaller steps very quickly
[how many figures? Does it go into 2 digits? No? then into three?
.....], but still going through them, and needing a good knowledge of
multiplication tables and other such properties of numbers to make it
easier.

.

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