# Thread: Transposition of formula/ fundamentals

1. ## Transposition of formula/ fundamentals

Hey, I am currently brushing up my maths skills, in preparation for a self taught engineering degree. I keep finding small mathematical rules that I have never come across, so I guess I need help filling in the gaps. Here is an example.

I understand everything up to the last step, I understand that you divide both sides by r, but why does the division only apply to the v on the right hand side, and not the entire v(1-s/100)?
I know I'm probably missing some fundamental math rules that would make this seem like a simple and trivial question, but if someone could kindly explain why, or even point me to some relevant materials to look at, I would be greatly appreciative.
OK also in my quest to solve this riddle, I have come across another little rule that I have not come across before.

So once again, I understand everything up to the 4th step, where the "+1" seems to vanish and become part of the dividend as "+q^2". Can anyone explain why this happens, and also maybe point me in the direction of some material to read.
Thanks!
Chris

2. ## Re: Transposition of formula/ fundamentals

Hi. For your first problem, have a look at this:

As for your second problem, we simply find a common denominator!

3. ## Re: Transposition of formula/ fundamentals

Originally Posted by risingdogfish
Hey, I am currently brushing up my maths skills, in preparation for a self taught engineering degree. I keep finding small mathematical rules that I have never come across, so I guess I need help filling in the gaps. Here is an example.

I understand everything up to the last step, I understand that you divide both sides by r, but why does the division only apply to the v on the right hand side, and not the entire v(1-s/100)?
It does apply to the whole thing: $\frac{v}{r}(1- s/100)$ is exactly the same as $\frac{1}{v}r(1- s/100)$ or $\frac{r(1- s/100)}{v}$

I know I'm probably missing some fundamental math rules that would make this seem like a simple and trivial question, but if someone could kindly explain why, or even point me to some relevant materials to look at, I would be greatly appreciative.
OK also in my quest to solve this riddle, I have come across another little rule that I have not come across before.

So once again, I understand everything up to the 4th step, where the "+1" seems to vanish and become part of the dividend as "+q^2". Can anyone explain why this happens, and also maybe point me in the direction of some material to read.
Thanks!
Chris
It's just what you learned in third or fourth grade arithmetic- to add fractions, get a common denominator and add the numerators:
$\frac{2ghA_1^2}{q^2}+ 1= \frac{2ghA_1^2}{q^2}+ \frac{q^2}{q^2}= \frac{2ghA_1^2+ q^2}{q^2}$.