Results 1 to 10 of 10

Math Help - Very simple fraction

  1. #1
    Senior Member Mukilab's Avatar
    Joined
    Nov 2009
    Posts
    468

    Very simple fraction

    Can \frac{3+x}{3} be simplified to \frac{x}{3}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member mathemagister's Avatar
    Joined
    Feb 2010
    Posts
    191
    Quote Originally Posted by Mukilab View Post
    Can \frac{3+x}{3} be simplified to \frac{x}{3}
    No, because \frac{3+x}{3} = \frac{3}{3}+\frac{x}{3} = 1 + \frac{x}{3}.

    You can't just get rid of the 3 in the numerator.

    Hope that helps

    Mathemagister
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,099
    Thanks
    67
    Quote Originally Posted by Mukilab View Post
    Can \frac{3+x}{3} be simplified to \frac{x}{3}
    Sure...but your final solution will be incorrect
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by Mukilab View Post
    Can \frac{3+x}{3} be simplified to \frac{x}{3}
    If x approaches infinity,

    then \frac{x+3}{3} will be indistinguishable from \frac{x}{3}

    in other words x has to be so large that x is "no different" from x+3
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by Archie Meade View Post
    If x approaches infinity,

    then \frac{x+3}{3} will be indistinguishable from \frac{x}{3}

    in other words x has to be so large that x is "no different" from x+3
    Along these lines we would write that, for "large" x (in fact, for x with "large" absolute value),

    \frac{x+3}{3} \approx \frac{x}{3}

    If this is part of some larger, more complicated equation, it may be useful to replace the original expression with an approximation. This practice is often done when modeling actual data in the sciences.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member mathemagister's Avatar
    Joined
    Feb 2010
    Posts
    191
    Quote Originally Posted by undefined View Post
    Along these lines we would write that, for "large" x (in fact, for x with "large" absolute value),

    \frac{x+3}{3} \approx \frac{x}{3}

    If this is part of some larger, more complicated equation, it may be useful to replace the original expression with an approximation. This practice is often done when modeling actual data in the sciences.
    A more mathematically tight way of writing that would be

    \lim_{x\rightarrow \pm \infty} \frac{3+x}{3} = \lim_{x\rightarrow \pm \infty} \frac{x}{3}
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Mukilab View Post
    Can \frac{3+x}{3} be simplified to \frac{x}{3}
    Let x = 1 in your proposed simplification. Does 4/3 = 1/3?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,099
    Thanks
    67
    Thanks Mr F.
    WHY spend time (even 1 second) in trying to somehow reason out
    that (a + b) / b = a / b ....
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by Wilmer View Post
    Thanks Mr F.
    WHY spend time (even 1 second) in trying to somehow reason out
    that (a + b) / b = a / b ....
    Haha, I thought the amount of discussion generated by the original post was pretty silly too, but Archie Meade's post seemed like an interesting spin to me (like in those lateral thinking problems that I also often find silly, but can have interesting solutions), which I thought was worth a little extra commentary, and apparently mathemagister felt a little more extra commentary was appropriate in response to my post, which contributed to this thread being ridiculously long. Next we'll be discussing how the proposed simplification relates to the Riemann hypothesis and P vs NP.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Senior Member
    Joined
    Jul 2009
    From
    Melbourne
    Posts
    272
    Thanks
    4
    You can only cancel fractions when 2 numbers/pronumerals are multiplied. You can't do it when their added or subtracted
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simple fraction derivative.
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 25th 2011, 04:45 PM
  2. simple fraction issue
    Posted in the Algebra Forum
    Replies: 12
    Last Post: May 2nd 2011, 03:34 AM
  3. simple fraction
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 27th 2010, 09:52 PM
  4. simple fraction question
    Posted in the Algebra Forum
    Replies: 5
    Last Post: March 19th 2009, 07:17 PM
  5. Simple Fraction Integration
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 8th 2008, 07:33 AM

Search Tags


/mathhelpforum @mathhelpforum