Basic Mathematics for College Students

Caution! When converting lengths, if no common units appear in the

numerator and denominator to remove, you have chosen the wrong

conversion factor.

Sometimes we must use two (or more) unit conversion factors to eliminate the

given units while introducing the desired units. The following example illustrates this

concept.

446 Chapter 5 Ratio, Proportion, and Measurement

Self Check 4

Convert 1 feet to inches.

Now TryProblem 39

(^12)
EXAMPLE 4
Convert feet to inches.
StrategyWe will multiply feet by a carefully chosen unit conversion factor.
WHYIf we multiply by the proper unit conversion factor, we can eliminate the
unwanted units of feet and convert to inches.
Solution
To convert from feet to inches, we must choose a unit conversion factor whose
numerator contains the units we want to introduce (inches), and whose
denominator contains the units we want to eliminate (feet). Since there are
12 inches per foot, we will use
To perform the conversion, we multiply.
Write as an improper fraction:.
Then multiply by a form of 1:.
Multiply the fractions.
Simplify.
1 34 feet is equal to 21 inches.
 21 in.
To simplify the fraction, factor 12. Then remove the common
 (^) factor of 4 from the numerator and denominator.

7  3  4

1

4

1

 1

in.



7 # 12

4 # 1

in.

Remove the common units of feet from the numerator and

 (^) denominator. Notice that the units of inches remain.

7

4

ft

12 in.

1 ft

12 in.

1 ft

1 43 1 43  47

1

3

4

ft

7

4

ft#

12 in.

1 ft

This is the unit we want to introduce.

 This is the unit we want to eliminate (the original unit).

12 in.

1 ft

1

3

4

1

3

4

EXAMPLE (^5) Football A football field (including both end zones) is
120 yards long. Convert this length to miles. Give the exact answer and a decimal
approximation, rounded to the nearest hundredth of a mile.
120 yd
(^1020) 30 40 50 40 30 20 10
10 20 40 30 30 40 50 (^2010)
Self Check 5
MARATHONSThe marathonis a
long-distance race with an official
distance of 26 miles 385 yards.
Convert 385 yards to miles.
Give the exact answer and a
decimal approximation, rounded
to the nearest hundredth of a
mile.
Now TryProblem 43