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2.3
Evaluating a Formula
P
urpose
The role this topic plays in quantitative reasoning
The most common quantitative exercise is evaluating a result based upon a formula where values are
substituted for the formula’s variables. In fact, mathematical models are fundamental in many disciplines
and these models are most often a formula or a series of formulas. Once you understand how to evaluate and
manipulate formulas, you will not only have the confidence to take full advantage of the useful formulas
available in the world around you, but also be able to trust that your resulting calculations are correct.
L
earning Goals
What you should learn while completing this activity
1. Correctly set up a mathematical model or use the correct formula.
2. Evaluate formulas (algebraic expressions) given values for some or all of the variables.
3.
Document
and explain the role of units in evaluating formulas and validating the results.
D
iscovery
Finding out for yourself
In exploring the world around you, consider that many common activities could be represented by
formulas: How much do you spend at the grocery store weekly? How much did you get paid this month?
How much does each member of a group have to contribute for paying the dinner check? How did you
balance and validate that your checkbook is correct? How do you calculate your current GPA? Can you
write and use a formula to make each of these calculations? As stated in the title of this experience, what
does it really mean to
evaluate a formula
?
W
hat Do You Already Know?
Tapping into your existing knowledge
1.
What is a formula?
2. What formulas have you used in the past?
3. If a formula has three variables, and you want to “evaluate the formula,” for how many of the variables
do you need to know values?
4. What is the Order of Operations?
5. What is a code word or phrase (mnemonic) you can use to help yourself remember the Order of
Operations?
M
athematical Language
Terms and notation
formula
— defines a quantity that can be calculated by providing specific value(s) for all the
variables in the defined expression
unit analysis
— when evaluating a formula, you can check your work by carrying the units of each
number through the formula. If your evaluation is correct, then some units should divide
out, leaving you with the correct units for the answer. This form of validation is called
unit
analysis
or
dimensional analysis
.