Applications

When we use formulas in our fields, sometimes we’ll sketch out an idea on a sheet of paper and plug numbers in to the formula to look at one specific location or condition. More often, we have data we’ve collected in the field, and we enter it into a spreadsheet or database to run calculations efficiently.

For example, chlorine needs to be added to a water treatment plant at a concentration sufficient to kill harmful bacteria. The chlorine will be added in pounds per day and we want to know the concentration over varying volumes of water treated per day (in million gallons per day).

[latex]L = 8.34QC[/latex]

So, if we add 50 lbs of chlorine per day for the month of June, can we arrange this formula to give us the concentration of chlorine over over discharges ranging from 1 to 4 million gallons per day?

Rearranging formulas relies on the rules we learned for algebra. Let’s recap a few of those here.

1. We rearrange a formula to “solve for” one of the variables. This means the target variable will be alone on one side of the equation and everything else will be on the other side.
2. Whatever you do to one side of an equation needs to be done to the other side.
3. It’s often easiest to start by “clearing” any fractions by multiplying both sides of the equation by the denominator.
4. We may also need to deal with a square root at this point. Wait until everything is under the square root symbol on one side  before squaring each side of the equation to remove the square root (if needed).
5. Then, in general, we “undo” addition or subtraction by adding (for subtraction) or subtracting (for addition).
6. Next, we separate variables from their coefficients (undo multiplication) by dividing.
7. Finally, if our target variable is squared, we’ll get it alone by taking the square root of both sides.

All of the formulas we use are applied – so they are numbers that are a measurement or count of something real. This means we will need to keep track of the units that we input into a formula and what we will get out of the formula with the units we are using.

For some students rearranging formulas is the easiest math we do all quarter and for others it’s the most challenging. If this sort of math gets frustrating for you – and you aren’t dealing with a spreadsheet – you can work a single problem by plugging each of the numbers in for the known variables and working with numbers rather than letters. We’ll look at how this works in the examples below.