Simple equation rearrange

Jossy

New member
Hi. I have a formula where E = (100/TR) - (100/MP). I'm trying to rearrange this so that I get MP = "..."

I got as far as 100/MP = (100/TR) - E but couldn't figure out what I needed to do to each side of the equation to close this out. I fear I may be going in the wrong direction anyway...

Thanks in advance for any help. Jossy

MarkFL

Super Moderator
Staff member
Hello, and welcome to FMH!

Your first step is going in the right direction. Next, combine the two terms on the RHS, and then you can invert both sides, and finally multiply by 100.

Jossy

New member
Thanks Mark! Sadly I may need a little more help than that! When you say combine, what do you mean? Also invert both sides? I get multiply by 100

MarkFL

Super Moderator
Staff member
Okay, what you've got so far is:

$$\displaystyle \frac{100}{MP}=\frac{100}{TR}-E$$

In order to combine the two terms on the right, we need a common denominator:

$$\displaystyle \frac{100}{MP}=\frac{100}{TR}-E\cdot\frac{TR}{TR}$$

$$\displaystyle \frac{100}{MP}=\frac{100-E\cdot TR}{TR}$$

Now we can invert (flip) both sides:

$$\displaystyle \frac{MP}{100}=\frac{TR}{100-E\cdot TR}$$

And finally, multiply both sides by 100:

$$\displaystyle MP=\frac{100TR}{100-E\cdot TR}$$

Does that make sense?

Jossy

New member
Perfect! And I even understand Thanks a million!

lookagain

Senior Member
I have a formula where E = (100/TR) - (100/MP). I'm trying to rearrange this so that I get MP = "..."
Is TR one variable, and is MP one variable? If "yes" is the answer, then you can continue in the thread as before with the users' guidance.
But if T, R, M, and P represent four variables, then you must use grouping symbols around them when written out in horizontal style.
If the latter is the case, at a minimum you need something such as this:

E = 100/(TR) - 100/(MP)

Or, if you want added emphasis, you could add extra grouping symbols for separation:

E = [100/(TR)] - [100/(MP)]