pre-algebra. using customary units of measure (5-5)
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PRE-ALGEBRA
PRE-ALGEBRA
Using Customary Units of Measure (5-5)
PRE-ALGEBRA
What are the customary units of measure?
The customary units of measure are the units of measure we mainly use in the U.S.
Using Customary Units of Measure (5-5)
PRE-ALGEBRA
How do choose an appropriate unit of measure?
To choose an appropriate unit to measure things, use units that aren’t to big (require fractions / decimals) or to small (require writing huge numbers)
Using Customary Units of Measure (5-5)
PRE-ALGEBRA
Choose an appropriate unit of measure. Explain
your choice.
a. weight of a hummingbird
b. length of a soccer field
Measure its weight in ounces, because a hummingbird is very light.
Measure its length in yards, because it is too long to measure in feet or inches and too short to measure in miles.
Using Customary Units of MeasurementLESSON 5-5
Additional Examples
PRE-ALGEBRA
What is a “unit analysis”?
How do you use dimensional analysis to solve conversion problems in which you need to change the units in a rate?
unit analysis (also called “dimensional analysis”): the process of changing units using conversion factors (unit rates in the form of fractions that include both the rate in the problem and the desired rate you want to “convert”, or change, to)
To use dimensional analysis, start with the units. Multiply the given rate by conversion fractions in which the desired units cancel out so that only the desired units are left (Example: To change the numerator unit if a rate, multiply by a conversion factor in which the new units are on top and the old units are on the bottom. To change the denominator unit of a rate, multiply by a conversion factor in which new units are on the bottom and the old units are on the top ).
Example: To change hours to minutes, you can multiply the number of hours by the “conversion factor” that changes the units as in:
3 hours = x = = 180 minutes
Example: To change minutes to hours, you can multiply the number of hours by the “conversion fraction” as in:
300 minutes = x = 5 hours
60 minutes 1 hour
1 hour60 minutes
Using Customary Units of Measure (5-5)
PRE-ALGEBRA
Use a conversion factor to convert 68 fluid ounces to
cups.
68 fl oz = •Use a conversion factor that changes fluid ounces to cups.
68 fl oz 1
1 c8 fl oz
17
= Divide the common factors and units.68 fl oz • 1 c 8 fl oz2
17 2 = c Simplify.
= 8 c Write as a mixed number.12
There are 8 c in 68 fl oz.12
Using Customary Units of MeasurementLESSON 5-5
Additional Examples
PRE-ALGEBRA
Fred’s fruit stand sells homemade lemonade in 6 -pint
bottles for $1.99. Jill’s fruit stand sells homemade lemonade in
3 -qt containers for the same price. At which stand do you get
more lemonade for your money?
12
12
Since 7 pints > 6 pints, you get more lemonade for your
money at Jill’s stand.
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3 qt = qt • Use a conversion factor that changes quarts to pints
12
72
2 pt1 qt
= • Divide the common factors and units. Usedimensional analysis to check the units.
1 2 pt1 qt
7 qt 2 1
= 7 pt Multiply.
Using Customary Units of MeasurementLESSON 5-5
Additional Examples
PRE-ALGEBRA
A wilderness group completes a 15,000-meter
hike in 5.2 hours. Find the group’s rate in meters per minute.
Write the rate and multiplyby the conversion factor.
15,000 m 5.2 h
= 15,000 m 5.2 h •
1h60 min
= 15,000 m 5.2 h •
1h60 min
Divide the common units.
≈ 48.1 m/min Simplify. Write the correct units.
LESSON 5-5
Additional Examples
Using Customary Units of Measurement
PRE-ALGEBRA
Convert 0.7 mi to feet.
There are 3,696 feet in 0.7 miles.
= 3,696 ft Simplify.
Because 5,280 ft = 1 mi, use the conversion factor .5,280 ft1 mi
0.7 mi = •0.7 mi
15,280 ft
1 miMultiply by the conversion factorand divide the common units.
LESSON 5-5
Additional Examples
Using Customary Units of Measurement
PRE-ALGEBRA
The fastest recorded speed for an eastern gray kangaroo
is 40 mi per hour. What is the kangaroo’s speed in feet per
second?
The kangaroo’s speed is about 58.7 ft/s.
40 mi.1 h
40 mi1 h
5280 ft1 mi
1 h 60 min
• •
LESSON 5-5
Additional Examples
Use appropriate conversion factors•
• •
1 min60 sec
• = 211,200 ft3,600 sec =
58.6 ft1 sec
3,6003,600
Using Customary Units of Measurement
PRE-ALGEBRA
The director of a political campaign has a project that will
take 90 volunteer-hours. The project must be completed in 6
hours. How many volunteers will the director need?
90 ÷ 6 = 15Divide the volunteer-hours by thenumber of hours.
The project requires 15 volunteers.
volunteer • hourshours
= volunteers Divide the common units and simplify.
The question asked for the number of volunteers, so the answer is reasonable.
Check for Reasonableness Use dimensional analysis tocheck the units of your answer.
LESSON 5-5
Additional Examples
Using Customary Units of Measurement
PRE-ALGEBRA
Choose an appropriate unit of measure. Explain your choice.
1. weight of a dog
2. length of a football field
3. Use a conversion factor to change 1 mi to ft.
Pounds; dogs are too heavy to measure in ounces and too light to measure in tons.
Yards; it is too long to measure in feet or inches and too short to measure in miles.
7,920 ft
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Lesson Quiz
Using Customary Units of MeasurementLESSON 5-5