1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Adding 1 to the denominator of each fraction in a sequence of increasing fractions

  1. Oct 21, 2012 #1
    Hello friends,

    I am attempting to solve this problem for a sorting algorithm with a lot of elements in fraction form (I'm avoiding floating point operations). My question is:

    Given a sequence of increasing fractions, does adding 1 to the denominator affect the ordering of th sequence?

    Given the sequence for example:

    1/5, 3/4, 8/10 ... a/b, x/y where x/y > a/b

    If I add 1 to thye denominator:

    1/(5+1) , 3 / (4+1), 8 / (10+1) ... a /(b+1), x/(y+1)

    is the order of the sequence preserved?

    thanks!
     
  2. jcsd
  3. Oct 21, 2012 #2

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Re: Adding 1 to the denominator of each fraction in a sequence of increasing fraction

    You said the fractions are increasing so this might not be an issue but..

    How do you treat fractions that are equivalent eg 1/2 and 4/8. If you rank 4/8 before 1/2 then the order would change.
     
  4. Oct 21, 2012 #3

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Re: Adding 1 to the denominator of each fraction in a sequence of increasing fraction

    How about the sequence...

    9/19, 1/2 which is 0.474 , 0.5 so increasing as per your rule.

    becomes
    9/20, 1/3 which is 0.45 , 0.333 which is decreasing
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Adding 1 to the denominator of each fraction in a sequence of increasing fractions
  1. Vapor Fraction (Replies: 1)

Loading...