Help understanding the solution to this fraction problem.

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Discussion Overview

The discussion revolves around understanding a fraction problem involving the positions of marks on a stick represented by the fractions M/7 and L/13. Participants seek clarification on the logical derivation of these fractions and their relevance to finding a specific point between them.

Discussion Character

  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant, limac, expresses confusion about the meaning of M/7 and L/13 and how they relate to the solution of the problem.
  • Another participant explains that k/7 and l/13 represent positions of marks on a stick, with k being an integer from 1 to 6 and l from 1 to 12.
  • The explanation includes that the point (k + l)/20 is where the stick is cut, indicating a specific location between the red and green marks.
  • limac later acknowledges understanding that (k + l)/20 represents the point between the respective marks, indicating a shift in comprehension.

Areas of Agreement / Disagreement

Participants appear to reach a mutual understanding regarding the representation of marks and the significance of the point (k + l)/20, although initial confusion existed about the fractions.

Contextual Notes

The discussion does not clarify the assumptions behind the choice of integers k and l or the implications of the fractions M/7 and L/13 beyond their representation as positions on the stick.

Who May Find This Useful

Individuals interested in fraction problems, mathematical reasoning, or those seeking clarification on similar conceptual challenges may find this discussion beneficial.

limac
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Hi,

Please see the attachment.

I really don't understand what the M/7 and the L/13 represents. How did he(authors) logically derive to that? And also, I don't understand how finding the value in-between M/7 and L/13 (M+L/20) helps them come up with the solution and the proof.

Thank you,
limac
 
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Where is the attachment?
 
Here, How about this?
 

Attachments

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Given an integer k from 1 to 6, and an integer l from 1 to 12, k/7 and l/13 are positions of a red mark and a green mark, respectively (where the stick goes from 0 to 1). The idea is that in between any red mark and any green mark, there is a point at (k + l)/20 where the stick is cut (since the stick is cut at 1/20 intervals).
 
adriank,

Alright, so k and l are representing anyone valid mark at a time on the stick. And (k+l)/20 is the point in-between any two of the respective red and green marks, right?

Now, it is making sense to me. I was very confused about what k/7 and l/13 meant.

Thank you very much for your time. :)
 

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