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#1 2013-07-27 07:09:53

atran
Member
Registered: 2013-07-12
Posts: 91

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

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...

Last edited by atran (2013-07-27 07:10:27)

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#2 2013-07-27 11:36:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,083

Re: Quotient, Ratio, Fraction; What's the difference?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2013-07-28 03:11:57

atran
Member
Registered: 2013-07-12
Posts: 91

Re: Quotient, Ratio, Fraction; What's the difference?

Thanks for the links.

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.

Last edited by atran (2013-07-28 03:15:03)

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#4 2013-07-28 03:16:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,083

Re: Quotient, Ratio, Fraction; What's the difference?

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


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2013-07-28 03:25:14

atran
Member
Registered: 2013-07-12
Posts: 91

Re: Quotient, Ratio, Fraction; What's the difference?

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?

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#6 2013-07-28 03:29:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,083

Re: Quotient, Ratio, Fraction; What's the difference?

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.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#7 2013-07-28 05:30:08

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,288

Re: Quotient, Ratio, Fraction; What's the difference?

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

View Image: fractions.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#8 2013-07-28 06:05:50

atran
Member
Registered: 2013-07-12
Posts: 91

Re: Quotient, Ratio, Fraction; What's the difference?

Now I got it, thanks...

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