Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Find each unit rate. 1. Jump rope 192
times in 6 minutes 2. Four pounds of bananas for
2.36 3. 16 anchor bolts for 18.56 4. 288
movies on 9 shelves
32 jumps/min
0.59/lb
1.16/bolt
32 movies/shelf
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Problem of the Day Replace each with a digit
from 0 to 6 to make equivalent ratios. Use each
digit only once.



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Learn to use one or more conversion factors to
solve rate problems.
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Insert Lesson Title Here
Vocabulary
conversion factor
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You can measure the speed of an object by using a
strobe lamp and a camera in a dark room. Each
time the lamp flashes, the camera records the
objects position.
Problems often require dimensional analysis, also
called unit analysis, to convert from one unit to
another.
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To convert units, multiply by one or more ratios
of equal quantities called conversion factors.
For example, to convert inches to feet you would
use the ratio below as a conversion factor.
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Multiplying by a conversion factor is like
multiplying by a fraction that reduces to 1,
such as .
5 5
12 in. 12 in.
1 ft 1 ft

, or

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(No Transcript)
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Additional Example 1 Finding Conversion Factors
Find the appropriate factor for each conversion.

• A. feet to yards
• B. pounds to ounces

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Insert Lesson Title Here
Try This Example 1
Find the appropriate factor for each conversion.

• A. minutes to seconds
• B. hours to days

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Additional Example 2 Using Conversion Factors to
Solve Problems
The average American uses 580 pounds of paper per
year. Find the number of pounds of paper the
average American uses per month, to the nearest
tenth.
The problem gives the ratio 580 pounds to 1 year
and asks for an answer in pounds per month.
Multiply the ratio by the conversion factor
Cancel yr units.
Divide 580 by 12.
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Additional Example 2 Continued
The average American uses 580 pounds of paper per
year. Find the number of pounds of paper the
average American uses per month, to the nearest
tenth.
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Insert Lesson Title Here
Try This Example 2
Sam drives his car 23,000 miles per year. Find
the number of miles he drives per month.
The problem gives the ratio 23,000 miles to 1
year and asks for an answer in miles per month.
Multiply the ratio by the conversion factor
Cancel yr units.
Divide 23,000 by 12.
Sam drives his car about 1917 miles per month.
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Additional Example 3 Problem Solving Application
A car traveled 60 miles on a road in 2 hours. How
many feet per second was the car traveling?
The problem is stated in units of miles and
hours. The question asks for the answer in units
of feet and seconds. You will need to use several
conversion factors.
List the important information
5280 ft 1 mi
Miles to feet
Hours to minutes
1 min 60 s
Minutes to seconds
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Additional Example 3 Continued
Multiply by each conversion factor separately, or
simplify the problem and multiply by several
conversion factors at once.
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First, convert 60 miles in 2 hours into a unit
rate.
60 mi 2 h
(602) mi (22) h
30 mi 1 h


Create a single conversion factor to convert
hours directly to seconds
1 min 60 s
hours to seconds

Set up the conversion factors.
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Solve
Do not include the numbers yet.
Notice what happens to the units.
Multiply.
44 ft 1 s
The car was traveling 44 feet per second.
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Look Back
A rate of 44 ft/s is less than 50 ft/s. A rate
of 60 miles in 2 hours is 30 min/h or 0.5 mi/min.
Since 0.5 mi/min is less than 3000 ft/ 60 s or 50
ft/s and 44 ft/s is less than 50 ft/s, then 44
ft/s is a reasonable answer.
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Try This Example 3
A train traveled 180 miles on a railroad track in
4 hours. How many feet per second was the train
traveling?
The problem is stated in units of miles and
hours. The question asks for the answer in units
of feet and seconds. You will need to use several
conversion factors.
List the important information
5280 ft 1 mi
Miles to feet
Hours to minutes
1 min 60 s
Minutes to seconds
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Try This Example 3 Continued
Multiply by each conversion factor separately, or
simplify the problem and multiply by several
conversion factors at once.
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First, convert 180 miles in 4 hours into a unit
rate.
180 mi 4 h
(180 4) mi (4 4) h
45 mi 1 h


Create a single conversion factor to convert
hours directly to seconds
1 min 60 s
hours to seconds

Set up the conversion factors.
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Solve
Do not include the numbers yet.
Notice what happens to the units.
Multiply.
66 ft 1 s
The train was traveling 66 feet per second.
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Look Back
A rate of 66 ft/s is more than 50 ft/s. A rate
of 180 miles in 4 hours is 45 mi/h or 0.75 mi/min.
Since 0.75 mi/min is more than 3000 ft/60 s or 50
ft/s and 66 ft/s is more than 50 ft/s, then 66
ft/s is a reasonable answer.
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Additional Example 4 Physical Science Application
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Additional Example 4 Continued
It may help to eliminate the fraction first.
Multiply top and bottom by 100.
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Additional Example 4 Continued
Now convert centimeters to meters.
5200 cm 1 s
Multiply by the conversion factor.
The object is traveling 52 m/s.
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Try This Example 4
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Try This Example 4 Continued
It may help to eliminate the fraction first.
Multiply top and bottom by 100.
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Try This Example 4 Continued
Now convert centimeters to meters.
6500 cm 1 s
Multiply by the conversion factor.
The object is traveling 65 m/s.
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Additional Example 5 Transportation Application
The rate 1 knot equals 1 nautical mile per hour.
One nautical mile is 1852 meters. What is the
speed in kilometers per hour of a ship traveling
at 5 knots?
5 knots 5 nautical mi/h
Examine the units.
The ship is traveling 9.26 km/h.
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Try This Example 5
The rate 1 knot equals 1 nautical mile per hour.
One nautical mile is 1852 meters. What is the
speed in kilometers per hour of a ship traveling
at 9 knots?
9 knots 9 nautical mi/h
Examine the units.
The ship is traveling about 16.67 km/h.
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Insert Lesson Title Here
Lesson Quiz
Find the appropriate factor for each
conversion. 1. kilograms to grams 2. pints to
gallons 3. You drive 136 miles from your house to
your aunts house at the lake. You use 8 gallons
of gas. How many yards does your car get to the
gallon? 4. A cheetah was timed running 200 yards
in 6 seconds. What was the average speed in miles
per hour?
1000 g kg
1 gal 8 pt
29,920 yd gal
68 mi/h