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Posers and Puzzles

Posers and Puzzles

  1. 25 May '05 01:09 / 1 edit
    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 top of the second fraction by 2 over the bottom half times 2. but if you multiply something by 2 over 2, isn't that kind of just like multiplying it by one? 2/2= 1...

    2y+ 20 x 2
    -------- --
    1/2x+1.5 2... 2/2 is one, so why do we get a different fraction when multiplying by one?

    what about simplifying? how can you simplify something like 20/4 by dividing it by 2 on each side? 2/2 is one
  2. Standard member orfeo
    Missing 285 + 1
    25 May '05 03:29 / 1 edit
    Originally posted by Duck Duck Goose
    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
    The 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?

    20/4 = 5, and 10/2 = 5, and 5/1 = 5. The whole aim is to write something in the simplest way possible.

    There are no 'sides' to your 20/4 example, by the way, an EQUATION has sides.
  3. 25 May '05 10:51 / 1 edit
    but isn't 2/2 one? that way, when you multiply the fraction by 1, it doesn't change anything
  4. Standard member orfeo
    Missing 285 + 1
    25 May '05 11:02 / 1 edit
    Originally posted by Duck Duck Goose
    but isn't 2/2 one? that way, when you multiply the fraction by 1, it doesn't change anything
    EXACTLY! That's what I'm saying. What is your problem with that idea?

    You said in your first post, "you get a different fraction". It's a differently written fraction WITH THE SAME VALUE.

    Try putting any value of x in both of your fractions, you will get exactly the same answer.
  5. Standard member Hegemon
    A Lost Bobby
    25 May '05 13:22

    2y+20 2
    --------- x -
    .5x+1.5 2

    = 4y+40
    -------
    x+3

    you are doublying both the numerator and the denominator.

    what's the issue..
  6. Standard member Bowmann
    Non-Subscriber
    26 May '05 00:35
    What a plonker!
  7. 30 May '05 07:21
    Haha, at least he asks the question, I spose
  8. Standard member genius
    Wayward Soul
    31 May '05 19:11
    yeah-if you don't understand something, ask! not everyone's quite so rude as bowmann. in general, we're a friendly bunch. at times. every now and then. if you're very nice. and bring cookies...but you've gotta leave your cat at the door, okay?
  9. Standard member TheMaster37
    Kupikupopo!
    01 Jun '05 08:37
    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 well, like yours for example.

    Multiplying with 1 doesn't do anything, you're right about that. But i CAN change the way we write something. There are many way to write one single fraction. We resort to tricks like this to write them in the most convenient form.
  10. Standard member genius
    Wayward Soul
    01 Jun '05 09:25
    Originally posted by TheMaster37
    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.
    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),

    2 2^0.5
    ------- x -------
    2^0.5 2^0.5

    =2 x 2^0.5
    --------------
    . 2
    the two's cancel, so your left with 2^0.5. i still find that beautiful...
  11. 02 Jun '05 16:59
    Originally posted by genius
    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),

    2 2^0.5
    ------- x -------
    2^0.5 2^0.5

    =2 x 2^0.5
    --------------
    . 2
    the two's cancel, so your left with 2^0.5. i still find that beautiful...
    actualy this example isn't even as complex as that.
    x/(x^.5)=(x^.5)^2*(x^.5)^-1=(x^.5)^(2-1)=(x^.5)^1=x^.5