- Joined
- Aug 1, 2014

- Messages
- 650

- Reaction score
- 241

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?