Basic Mathematics for College Students

Writing a Rate as a Fraction

To write a rate as a fraction,write the first quantity mentioned as the numerator

and the second quantity mentioned as the denominator, and then simplify, if

possible.Write the units as part of the fraction.

420 Chapter 5 Ratio, Proportion, and Measurement

Self Check 7

GROWTH RATESThe fastest-

growing flowering plant on

record grew 12 feet in 14 days.

Write the rate of growth as

a fraction in simplest form.

Now TryProblems 49 and 53

EXAMPLE (^7) Snowfall According to the Guinness Book of World
Records,a total of 78 inches of snow fell at Mile 47 Camp, Cooper River Division,
Arkansas, in a 24-hour period in 1963. Write the rate of snowfall as a fraction in
simplest form.
StrategyWe will use a fraction to compare the amount of snow that fell (in
inches) to the amount of time in which it fell (in hours). Then we will simplify it.
WHYA rate is a quotient of two quantities with different units.
Solution
78 inches in24 hours can be written as.
Now, we simplify the fraction.
Since the units are different, they cannot be removed.
The snow fell at a rate of 13 inches per 4 hours.



13 inches

4 hours

To simplify, factor 78 as 6 13 and 24 as 4  6.

Then remove the common factor of 6 from the

numerator and denominator.

78 inches

24 hours



6

1

13 inches

4  6

1

hours



78 inches

24 hours



Find unit rates.

Unit Rate

A unit rateis a rate in which the denominator is 1.

To illustrate the concept of a unit rate, suppose a

driver makes the 354-mile trip from Pittsburgh to

Indianapolis in 6 hours. Then the motorist’s rate

(or more specifically, rate of speed) is given by

Since the units are different, they cannot be

 (^) removed. Note that the denominator is 1.
59 miles
1 hour
Factor 354 as 6 59 and remove the common
factor of 6 from the numerator and denominator.
354 miles
6 hours



6

1

59 miles

6

1

hours

5

Pittsburgh

Indianapolis

PENNSYLVANIA

INDIANA OHIO