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•  » Quotient, Ratio, Fraction; What's the difference?

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atran
2013-07-29 04:05:50

Now I got it, thanks...

bob bundy
2013-07-29 03:30:08

hi atran,

Let's say you have two cakes and you want to share these out equally between three people.

The diagram shows this happening and each person gets two thirds of a cake.

You can easily generalise this.

So getting the answer for  2 divided by 3 and the fraction 2/3 are the same thing.

Bob

bobbym
2013-07-29 01:29:23

Hi;

Thinking of it as 2 divided by 3 is just one way of looking at that is useful for getting the decimal representation.

I do not know where the part - whole idea comes from and I do not use it. If you are not having trouble with fractions thinking about them in your own way then I say that is fine.

atran
2013-07-29 01:25:14

I'm thinking like this: If the area of the cake is 1, then it's obvious that one third of the cake is (1/3), therefore two thirds is (2/3).

But it's a bit vague to me, why do the denominator and the numerator represent the whole and the part respectively? I mean, arithmetically, (2/3) means three divides two. From where does the part-to-whole interpretation of division comes from?

bobbym
2013-07-29 01:16:21

The whole cake is divided into 3 pieces ( the denominator ) You eat 2 of them ( the numerator ).

atran
2013-07-29 01:11:57

Say I want two thirds of a cake with the area, A. The expression for the wanted area becomes, 2A/3.
As for fractions, I don't understand why the denominator represents the whole and the numerator represents the part.

bobbym
2013-07-28 09:36:43
atran
2013-07-28 05:09:53

Hi,

Am I thinking right? Quotient is the result of division. Ratio relates one quantity to another. Fraction is ratio of two quantities of the same type.

Thanks...