Originally posted by Duck Duck GooseThe whole POINT of multiplying by, say, 2/2 is that you're not changing the value of something, just the way of writing it. What's paradoxical about that?
let's say that we have 2y+10 over x + 3. We need to add that fraction to 2y+20 over 1/2x + 1.5 . the logical thing to do would be to multiply the second fraction by 2 to get common denominators, right? so we should multiply the ...[text shortened]... y something like 20/4 by dividing it by 2 on each side? 2/2 is one
Originally posted by Duck Duck GooseEXACTLY! That's what I'm saying. What is your problem with that idea?
but isn't 2/2 one? that way, when you multiply the fraction by 1, it doesn't change anything
Originally posted by TheMaster37it can be very useful, for instance 2/(2^0.5), i.e. two divided by root two, is actually root two! miltiply by (2^0.5)/(2^0.5),
Yeah, we're friendly...
You'll agree that your second fraction is 'ugly'. To write is in a simpler form you have to do something to it, without changing the value of the fraction in all points x.
EG instead of writing 1/(1/2) you simply write 2. What we did here is multiply 1/(1/2) with 1=2/2. The same trick can be done to other fractions as we ...[text shortened]... te one single fraction. We resort to tricks like this to write them in the most convenient form.
Originally posted by geniusactualy this example isn't even as complex as that.
it can be very useful, for instance 2/(2^0.5), i.e. two divided by root two, is actually root two! miltiply by (2^0.5)/(2^0.5),
------- x -------
=2 x 2^0.5
the two's cancel, so your left with 2^0.5. i still find that beautiful...