Why Do Initial and Final Conditions Swap Places in Scientific Fractions?

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The discussion centers on the confusion surrounding the placement of initial and final conditions in scientific fractions related to various physical properties. Users express uncertainty about why different fractions, such as density and frequency, seem to have inconsistent logic regarding which condition goes in the numerator or denominator. It is suggested that this reflects the concepts of proportionality and inverse proportionality, where an increase in one variable can lead to a decrease in another. Clarification is sought on specific experiments to better understand the relationships between these variables. Overall, the conversation highlights the complexity of applying these principles in practical scenarios.
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numberator or denometer??

good lord. I am working on a lesson about instruments. and the the formula has a bunch of different fractions (eg/ tension fraction, length fraction, density fraction, etc.)

so they have one list of the "initial conditions" and then the other list of "final conditions".

and there seems to be no logic for the putting the initial or final conditions into the fractions.

like on question it'll suggest "since an increase in density results in a decrease in frequency, the density fraction will have the smaller density in the numerator"

and then on another question "since a decrease in density results in an increase in frequency, the density fraction will have a larger density in the numerator"

:confused:

~Amy
 
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I'm as confused as you are. I have no idea what experiment you or doing, and what density relates to what frequency. I might be able to help with more details.

As far as I can tell, it's just trying to show you how proportionality and inverse proportionality work. For example f(x) = g(x) * (h(x))^{-1} or also written f(x) = \frac{g(x)}{h(x)}. If we increase h(x) then f(x) will decrease because they are inversely proportional. If we increase g(x) then f(x) will increase because they are proportional.

Is this it? If not, more details.
 
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