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Q
uantitative
R
easoning &
P
roblem
S
olving
84
© 2014 Pacific Crest
M
ethodology
U
sing
U
nit
A
nalysis when
E
valuating a
F
ormula
Scenario:
5 feet
3 feet
Compute the perimeter of a rectangle with
a length of 3 feet and a width of 5 feet.
Step
Explanation
Watch it Work!
1. Identify the formula you
need to use
Use the right formula in its most useful
form.
P =
2(
L + W
)
2. Identify the units in the
problem
Make a list of all relevant units mentioned
in the problem. Identify which units
measure the same things.
feet
3. Substitute given values
for the variables
Include units as you make the
substitutions in the formula.
P =
2(3 feet + 5 feet)
4. Simplify units
Divide out any common units that appear
in both the numerator and denominator of
multiplied fractions.
no units to simplify
5. Convert to same units
Multiply by a fraction equal to 1 to make
units that measure the same thing match.
units already match
6. Simplify units
Divide out any common units that appear
in both the numerator and denominator of
multiplied fractions.
no fractions
7. Perform all operations
Keep the remaining units as you carry out
the operations.
P
= 2(8 feet) = 16 feet
8. Validate your answer
and its units
Work backwards from the answer to the
original values.
16 feet = 2(
L
+
W
)
16 feet = 2(3 feet +
W
)
16 feet = 6 feet + 2
W
10 feet = 2
W
W
= 5 feet
Scenario:
Find the distance traveled if a car is driving 50 miles per hour for 90 minutes.
Step
Watch it Work!
1. Identify the formula you
need to use
d rt
=
2. Identify the units in the
problem
miles, hours, minutes; hours and minutes both measure time