Sorting Fractions: Does Adding 1 to the Denominator Affect Order?

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SUMMARY

The discussion centers on the impact of adding 1 to the denominator of fractions on their order in a sequence. It is established that for a sequence of increasing fractions, adding 1 to the denominator can disrupt the order, as demonstrated with examples such as 9/19 and 1/2, which become 9/20 and 1/3, respectively. The participants highlight the importance of considering equivalent fractions, as their ranking can further complicate the preservation of order. Overall, the conclusion is that adding 1 to the denominator does not guarantee that the order of the sequence remains intact.

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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!
 
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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.
 


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
 

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