Pre-Algebra Chapter 6 - Ramsey School District

Study Tip
Look Back
To review dimensional
analysis, see Lesson 5-3.
To convert a rate such as miles per hour to a rate such as feet per second,
you can use dimensional analysis. Recall that this is the process of carrying
units throughout a computation.
Example 4
Convert Rates
ANIMALS A grizzly bear can run 30 miles in 1 hour. How many feet
is this per second?
You need to convert 30 mi
to ft
. There are 5280 feet in 1 mile and
1 h 1s
3600 seconds in 1 hour. Write 30 miles per hour as 30 mi
.
1 h
30 m
1
i
h
30 m
1 i
h
5 280
1 m
ft
i
36 00s
1 Convert miles to feet and hours to seconds.
h
30 m
1
i
h
5 280
ft 1 h
1 The reciprocal of 36 00s
1 h
is .
mi
36 00s
1 h 36 00s
1
44
30 mi 5280 ft 1 h
Divide the common factors and units.
1 h 1 mi 3600 s
120
44 1
ft
Simplify.
s
So, 30 miles per hour is equivalent to 44 feet per second.
Concept Check
Guided Practice
GUIDED PRACTICE KEY
1. Draw a diagram in which the ratio of circles to squares is 2:3.
2. Explain the difference between ratio and rate.
3. OPEN ENDED Give an example of a unit rate.
Express each ratio as a fraction in simplest form.
4. 4 goals in 10 attempts 5. 15 dimes out of 24 coins
6. 10 inches to 3 feet 7. 5 feet to 5 yards
Express each ratio as a unit rate. Round to the nearest tenth, if necessary.
8. $183 for 4 concert tickets 9. 9 inches of snow in 12 hours
10. 100 feet in 14.5 seconds 11. 254.1 miles on 10.5 gallons
Convert each rate using dimensional analysis.
12. 20 mi/h ft/min 13. 16 cm/s m/h
Application
GEOMETRY For Exercises 14 and 15, refer to the figure below.
14. Express the ratio of width to length as
6 cm
a fraction in simplest form.
15. Suppose the width and length are each
increased by 2 centimeters. Will the ratio
of the width to length be the same as the
ratio of the width to length of the original
rectangle? Explain.
10 cm
266 Chapter 6 Ratio, Proportion, and Percent