Proportionality/Ratios type question

[btdubs]

Hi there,

Not sure where to post this as this is a weird question, hope I'm in the right space. I'm prepping for a standardised test where isolating variables/getting rid of constants to find relationships between variables is a key skill. I've read the rules but I don't have specific questions as I am trying to practise the general skill itself. It looks something like this:



Question: If there is a negative sign in front of a variable, do I keep the negative sign in the proportionality relationship or get rid of it? I've been told conflicting things, and was under the assumption that I should be removing the negative sign.

 

[Dr.Peterson]

Hi there,

Not sure where to post this as this is a weird question, hope I'm in the right space. I'm prepping for a standardised test where isolating variables/getting rid of constants to find relationships between variables is a key skill. I've read the rules but I don't have specific questions as I am trying to practise the general skill itself. It looks something like this:

View attachment 33830

Question: If there is a negative sign in front of a variable, do I keep the negative sign in the proportionality relationship or get rid of it? I've been told conflicting things, and was under the assumption that I should be removing the negative sign.

View attachment 33832

Why can't both be true? If [imath]\lambda[/imath] is proportional to h, then it is also proportional to -h.

Normally, we start with a proportionality statement, and write an equation for it, rather than the reverse. Why do you need to choose one? Perhaps you need to show us an actual problem of the type you are trying to solve. (Specific examples can be the best way to ask general questions!)

 

[btdubs]

Why can't both be true? If [imath]\lambda[/imath] is proportional to h, then it is also proportional to -h.

Normally, we start with a proportionality statement, and write an equation for it, rather than the reverse. Why do you need to choose one? Perhaps you need to show us an actual problem of the type you are trying to solve. (Specific examples can be the best way to ask general questions!)

Thanks for getting back to me. I agree a specific question would be good to show, personally I haven’t come across one and thought I would clarify in case I do come across it in the exam.

The kind of question it would usually come up in would look like this:



In this case it has given us the proportionality relationship explicitly, but usually it would give me a formula and I would have to derive this relationship myself. For example:


I’ll try and make a question. They might ask how k2 changes if Ea increases, so I would get rid of the constants and isolate the variables Ea and k2 to find a relationship (in this case k2 proportional to Ea) so k2 will increase. On the flip side, I’m wondering what the relationship will be if there was a negative sign preceding Ea and what happens to k2 then, when Ea changes in that relationship.

I usually got rid of the negative sign due to this sentiment here on another website: https://math.stackexchange.com/questions/3204950/does-the-sign-matter-for-proportionality

 

[Dr.Peterson]

If you can't find an actual problem where this comes up, then I think you're inventing a nonexistent difficulty. I would ignore it unless it actually shows up somewhere.

Now, if you are asked for a numerical answer to a problem, or a formula, or whether something increases or decreases, rather than to state a proportionality, then of course you would keep the sign. It's only in the proportionality statement itself that the sign can be dropped (if you see a reason to) -- because the constant of proportionality as a whole is dropped. Elsewhere, it is part of the formula, and is needed.