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What is wrong with taking a half out as a factor and going

I know it's wrong, but I can't see exactly what is wrong with it, I would appreciate a detailed answer and not something like

thnx
Last edited by member910132; 21-05-2012 at 11:55.
(Original post by member910132)

What is wrong with taking a half out as a factor and going

I know it's wrong, but I can't see exactly what is wrong with it, I would appreciate a detailed answer and not something like

thnx
You can't really get a better explanation than the one you wouldn't like to be given.

Well, you could prove it to yourselve geometrically if you let a and b be the sides of a rectangle. Calculate its area (ab), and then shink each length by a half and calculate the new area (0.5a*0.5b) - you'll find that the new area is percisely one quarter of the original area, and not one half of the original area.
(Original post by oo00oo)
Well, you could prove it to yourselve geometrically if you let a and b be the sides of a rectangle. Calculate its area (ab), and then shink each length by a half and calculate the new area (0.5a*0.5b) - you'll find that the new area is percisely one quarter of the original area, and not one half of the original area.
Thnx, PRSOM !
(Original post by member910132)

What is wrong with taking a half out as a factor and going
You are just getting confused with sums and products, that is all.

(i) but

(ii) .

With a whole number, you demonstrate (i) by rearranging the left had side to give

where there are the same number of sums on each side.

On the other hand (ii) would look like

i.e. when you expand out the brackets you can think of a square array of the terms .