Solving a Fractional Equation: x/y=3/5

  • Context: High School 
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Discussion Overview

The discussion revolves around the equation \(\frac{x}{y}=\frac{3}{5}\) and the implications for the relationship between \(x\) and \(y\). Participants explore the conditions under which \(x\) is less than, greater than, or equal to \(y\), considering both positive and negative values for \(x\) and \(y\).

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant suggests that if \(x/y > 0\), then \(x\) and \(y\) must have the same sign, leading to the conclusion that if both are positive, then \(x < y\).
  • Another participant points out that if both \(x\) and \(y\) are negative, such as \(x = -3\) and \(y = -5\), then \(x/y = 3/5\) but \(x > y\).
  • Some participants emphasize that the relationship between \(x\) and \(y\) depends on their signs, reiterating the need to consider both positive and negative cases.
  • A later reply humorously questions the suggestion to "circle both" answers, noting that there were four options presented, including "none of these."

Areas of Agreement / Disagreement

Participants generally agree that the relationship between \(x\) and \(y\) is contingent on their signs, but multiple competing views remain regarding the specific outcomes based on those conditions.

Contextual Notes

The discussion does not resolve the implications of the fractional equation fully, as it relies on the assumptions about the signs of \(x\) and \(y\), which are not definitively established.

santa
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If [tex]\frac{x}{y}=\frac{3}{5}[/tex] then

(A) x<y ( B) x> y (C)x=y (D)noon of these
 
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none of these acually
x/y>0
=> x and y have same sign
if both r +ve
x<y
but if both r -ve
eg x=-3 , y=-5
then x/y=3/5
but
x>y
 
As aiglet said, it will depend if both numbers are positive or if both numbers are negative.

if in doubt, circle both =)
 
Invictious said:
As aiglet said, it will depend if both numbers are positive or if both numbers are negative.

if in doubt, circle both =)
Circle both? There were four answers, one of which was "none of these".
 

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