Results 1 to 8 of 8

Math Help - is it puzzle or complex problem?!

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    9

    is it puzzle or complex problem?!

    Math problem;

    "Jane made one out of two free throws in the first half and one out of three in the second. So, she made two out of five in the game."

    so, 1/2+1/3=2/5?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    Hello, turkmath!

    Jane made \tfrac{1}{2} of her free throws in the first half
    and \tfrac{1}{3} in the second half.

    So, she made two out of five in the game.

    so: \frac{1}{2} + \frac{1}{3} \:=\:\frac{2}{5} ? . . . . . You're kidding, right?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2008
    Posts
    9
    Quote Originally Posted by Soroban View Post
    Hello, turkmath!
    No, it is not kidding! for example one student ask it; is it correct? it is a famous scenario for elementary math teachers. The representation is correct for this problem?i only want to know true reason for this...
    Last edited by turkmath; January 25th 2009 at 05:50 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member euclid2's Avatar
    Joined
    May 2008
    From
    Ottawa, Canada
    Posts
    400
    Awards
    1
    Quote Originally Posted by turkmath View Post
    Math problem;

    "Jane made one out of two free throws in the first half and one out of three in the second. So, she made two out of five in the game."

    so, 1/2+1/3=2/5?
    incorrect
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2009
    Posts
    5

    absurd

    Let's, say, she threw 1 out 1 in the first game and 1 out of 1 in the second. By that logic of yours

    1/1 + 1/1 = 2/2.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    Hello, turkmath!

    No, it is not kidding!

    Too bad . . . It's gruesomely incorrect.

    By your reasoning, she will always average \tfrac{2}{5} \,=\,40\%


    First of all: . \frac{1}{2} + \frac{1}{3} \;=\;\frac{5}{6} . . . we can't add fraction like you did.


    Secondly, it depends on how many attempts were made in each half.


    Suppose in the first half, she made 5 out of 10 . . . That's \tfrac{1}{2}

    And in the second half, she made 10 out of 30 . . . That's \tfrac{1}{3}

    Then she made 15 out of 40 during the whole game . . . That's \frac{15}{40} \,=\,\frac{3}{8} \:=\:37\tfrac{1}{2}\%


    Suppose in the first half, she made 1 out of 2 . . . That's \tfrac{1}{2}

    And in the second half, she made 16 out of 48 . . . That's \tfrac{1}{3}

    Then she made 17 out of 50 during the whole game . . . That's \frac{17}{50}\:=\:34\%

    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Aug 2008
    Posts
    9
    Thanks for yours explanations. But we can add this way in some special rational numbers.

    a/b+c/d=a+c/b+d
    .
    .
    .

    ad^2+cb^2=0

    For example; if
    b=3, d=6 and a=-1 , c=4
    we can add this way
    -1/3+4/6=3/9...
    is it correct?your thinkings...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Jan 2009
    Posts
    5

    what is correct?

    Is -1/3+4/6=3/9 correct?

    Yest, it is.

    However, it is correct due to the common rules of the addition - and for no other reason.

    As Soroban noted, -1/3+4/6 = -1/3 + 6/9 which, acording to your rule would be 5/12 quite different from 3/9.

    Sometimes things come out correct for wrong reasons. This does not make wrong reasons right.

    For example,

    0.5 + 0.2*0.3 = (0.5 + 0.2)(0.5 + 0.3), or

    3^(2/3) * 9^(7/6) = (3*9)^(9/9) = 27.

    (The examples are from E. J. Barbeau, Mathematical Fallacies, Flaws, and Flimflam.)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sliding block puzzle problem
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: August 6th 2011, 07:49 AM
  2. Puzzle-like problem
    Posted in the Algebra Forum
    Replies: 8
    Last Post: January 15th 2011, 12:54 PM
  3. Puzzle problem
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: April 28th 2009, 11:57 PM
  4. fibonacci puzzle problem
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 3rd 2009, 05:41 PM
  5. complex square puzzle
    Posted in the Math Challenge Problems Forum
    Replies: 1
    Last Post: December 21st 2006, 09:22 AM

Search Tags


/mathhelpforum @mathhelpforum