R+S = P

mn

R+S = P

mn

Tutors, please sign in to answer this question.

The key to this problem is using inverse operations to get m by itself. (If you don't recall, inverse operations "undo" each other. Like + and -, or x and /.)

A tip to remember: when solving for a variable in the denominator, like your m, it is always helpful to get it in the numerator.

So to begin!

The problem is being **divided** by m, so to move it to the numerator you want to
**multiply** both sides of the equation by m. Remember, keep the equation equal by doing the same operation to each side.

It should look like this: m * (R + S)/(mn) = m * P

That will give you: (R + S)/n = mP

Notice the m's on the left "cancel" each other out. And you're actually almost done! We need to get m by itself and get rid of the P. m and P are
**multiplied **together, so to undo that, you should **divide** by P.

Should look like: (R + S)/n /P = mP /P

Now the P's on the right cancel, and you are left with: (R + S)/n /P = m

To make it look a little better: notice you are dividing R + S by both n and P. So we can put both n and P in the denominator of the fraction.

Final answer: (R + S)/(np) = m

First cross multiply Pmn = R + S

Finally divide both sides by Pn to get m = (R + S)/Pn

I usually circle the variable I am trying to solve for in each step, then use algebraic principles on both sides of the equation to isolate that variable

Cross multiplication works, but it usually adds extra steps. It's what you call a "brute force" method.

That being said, it is effective, just not always efficient!

## Comments