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

]]>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.

]]>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?

]]>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.

To get a definition look here:

http://www.mathsisfun.com/definitions/quotient.html

]]>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...

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