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Some basic arithmetic stuff regarding proportions and division.

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Necr0sis713

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So i'm beginning to notice that becoming proficient at simple arithmetic helps tremendously with some of the MCAT questions; nothing feels more annoying then getting a question wrong because you couldn't do the simple arithmetic.

So I have two questions that involve quick "mental" math:

First off. Proportional vs inversely proportional. While I understand what these mean, i'm having trouble wrapping my head around why certain equations mean that things are inversely proportional and directly proportional.

Take a look at Boyle's law (chemistry) for instance: P1V1=P2V2. This means that pressure and volume are inversely proportional right? I'm a little confused because I thought when things are multiplied they are directly proportional; or rather, things are inversely proportional if you divide them.

So let's say somebody tells me that the V2 goes up relative to V1. Why is it that P2 must be lower? I understand that both of sides have to equal each other out, so they have to "balance" per say. However, because there are variables being multiplied in this equation it seems rather counterintuitive to think if something goes up on one side then the other must go down. Would this mean that where there is more volume, there is less pressure?

My next question is in regards to division. I had a question on a question bank for the mcat that asked me to calculate the wavelength of sound when the velocity is 340 m/s and the frequency is 20,000 HZ. Obviously, this would be solved by doing velocity/frequency. However, how would I expect to figure this out by paper and pencil without a calculator. Could someone break down for me a simple and easy method to figure out what 340/20,000 would be STRICTLY without a calculator, like some sort of a shortcut or simple arithmetic trick?
 

Cawolf

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If you solve the equation for one variable, then the relationships make more sense.

340/20,000 = (34 x 10^1)/(2 x 10^4) = (34/2)(10/10^4) = 17 x 10^-3 = 0.017
 

Labrat07

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For your first questions, I think you got confused since the formular have the same notations. Let's make it simpler for you by having simple formular

AB = CD

So if C >>>>>A, what would happen to D compare to B??? or B compare to D? D would be smaller than B right? So as C increase , D decrease . Therefore , you called that inverse propotional

Play around with it a bit.

Then if A increase on the left side, what would have to happen on C or D? One have to increase as well. So you call this directly propotional.

Take it slow and try to understand. I hope that answer your question.
 
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Necr0sis713

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Perfect! So you're saying that A and C, for example are directly proportional.

While A and B are inversely proportional, correct?

Now lets say this was set up as A/B=C/D

Then that would mean A and D are directly proportional? and A and B are inversely proportional?
 

Cawolf

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A/B = C/D is just another way of writing AD = CB or A = CB/D (I prefer to solve for one variable).

So apply the logic posted by @Labrat07 to the above.

Consider these simple definitions:

Directionally proportional - As one variable increases, another increases at the same rate.
Inversely proportional - As one variable increases, another decreases at the same rate.

So in the above, when D increases, what happens to A? A will get smaller, so A and D are inversely proportional. When B increases, A will also increase, so A and B are directly proportional.
 
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