## A Conversation for Fractions

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Catwoman Started conversation Jul 12, 2001

An excellent entry. It probably makes me seem really sad to admit it but I actually rather enjoyed reading the entry the whole way through. More, please! How about ratio and proportion which, although mentioned in the 'Fractions' entry isn't fully covered, I think. Or maybe percentages and how to work with them. I'm sure that vast majority of people in this country (the UK) would struggle to work out the full price (ie 100%) of something given only a reduced price (say 75%).

"Well, that's easy," they say, "you just add on 25%." And then proceed to work out 25% of the reduced price ...

One little thing (and I know how hard it is to change edited entries, but) -

"The same fraction can be written with different denominators."

Hmmm. You need to tread very carefully with statements like that. Is 3/4 the *same* fraction as 6/8 or is it merely a representation of the same proportion? From a primary school teacher's point of view it's the latter.

Just like 3*8 gives the same answer as 4*6, they also are not the same, ie 3 rows of 8 isn't the same as 4 rows of 6, which is particularly relevant when trying to get 8 year olds to visualise multiplication.

Am I being too picky? Probably. In which case I apologise, because I still think it's a good entry, and I'm tempted to use it with my class when next I teach fractions.

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toybox Posted Dec 18, 2002

Are 3/4 and 6/8 the same? Well, if these are viewed are equivalence classes of the pairs of integers (3,4) and (6,8) modulo, well, some well-chosen equivalence relation, I daresay they are the same object.

In fact, I think they can be considered to be different as they don't ring the same bell, if I may say so. When I read 3/4 I imagine a pizza cut in four parts, three of which had been eaten. In 6/8 I imagine the same pizza cut in eight parts, six of which have been eaten, and there are two parts left (two smaller parts but two nonetheless).

It's always the same problem with maths, objects looking the same but being different or looking different but being the same. It's the same for functions, one should not consider two functions to be equal unless they have same domain and same codomain (the codomain in the target set). For example, the sine from the reals to the reals should be viewed not as the same function as the sine from the reals to [-1 1], say.

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