Re: Explaining a common fraction

On Thu, 26 Jan 2006 08:00:38 -0400, "BarryAC"
<barrymalvina@xxxxxxxxxxxxx> wrote:

>Thanks for your response, I hope the thread started explains. I have always
>accepted what you say, that is "c/d means c divided by d" and there is no
>problem, but as taught to children, it also means "divide your whole into d
>parts and take c of them". I am trying to understand why these are then the
>same. Barry AC.
>

When dividing by 4, you are finding the number of groups of four. So,
20 divided by four shows that there are five groups [or sets] of four.
As below:

20 things. How many groups of 4? Answer 20 / 4.

- - - - - - - - - - - - - - - - - - - -
20 things in 5 groups of 4.

To divide into groups is to partition. So you have what was called
"Aliquot parts." After this, it becomes a game of semantics. Either
the concept is clear, or it is not. On division [partitioning], there
may remain zero, or some part 'remaining'. Hence, the "Remainder".

- - - - - - - - - - - - - - - - - - - - - - -
20 things in 5 groups of 4 with 3 remaining: 20/4 = 5 R 3.

.

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