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9-3 Converting Customary Units
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
9-3 Converting Customary Units
Warm UpList the first five multiples of the following numbers.
1. 3 2. 12
3. 36 4. 48
3, 6, 9, 12, 15 12, 24, 36, 48, 60
36, 72, 108, 144, 180
48, 96, 144, 192, 240
9-3 Converting Customary Units
Problem of the Day
How much will it cost to build a fence that is 24 ft long, if it costs $20 to build a fence that is 15 ft long?$32
9-3 Converting Customary Units
Learn to convert customary units of measure.
9-3 Converting Customary Units
You can use the information in the table below to convert one customary unit to another.
When you convert one unit of measure to another, you can multiply by a conversion factor.
9-3 Converting Customary Units
Additional Example 1A: Using a Conversion Factor
Convert 9 yards to feet.
Set up a conversion factor.
Multiply using the conversion factor. Cancel the common unit, yd.
9 yd = 27 ft
9 yd
Think: yards to feet–3 feet = 1 yd, so use .3 ft 1 yd
3 ft 1 yd
Write the unit you are converting to in the numerator and the unit you are converting from in the denominator.
Caution!
9-3 Converting Customary Units
Additional Example 1B: Using a Conversion Factor
Convert 10,000 pounds to tons.
Set up a conversion factor.
Multiply 10,000 lbs by the conversion factor. Cancel the common unit, lbs.
10,000 lb = 5 tons
10,000 lb
Think: pounds to tons–1 ton = 2,000 lbs, so
use . 1 ton s 2,000 lbs
1 ton 2,000 lb
9-3 Converting Customary Units
Check It Out: Example 1A
Convert 3 quarts to pints.
Set up a conversion factor.
Multiply using the conversion factor. Cancel the common unit, qt.
3 quarts = 6 pints
3 qt
Think: quarts to pints–2 pints = 1 quart, so use
.
2 pt 1 qt
2 pt 1 qt
9-3 Converting Customary Units
Check It Out: Example 1B
Convert 15,840 feet to miles.
Set up a conversion factor.
Multiply 15,840 ft by the conversion factor. Cancel the common unit, ft.
15,840 feet = 3 miles
15,840 ft
Think: feet to miles–1 mile = 5,280 feet, so
use . 1 mile 5,280 ft
1 mi s 5,280 ft
9-3 Converting Customary Units
Another way to convert units is to use proportions.
A proportion shows that two ratios are equivalent. Use a conversion factor for one of the ratios.
Remember!
9-3 Converting Customary Units
Convert 3 quarts to cups.
Additional Example 2: Converting Units of Measure by Using Proportions
Convert quarts to cups.
1x = 12
1 • x = 4 • 3
3 quarts = 12 cups.
1 quart is 4 cups. Write a proportion. Use a variable for the value you are trying to find.The cross products are equal.Divide both sides by 1 to undo the multiplication.
3 qt = cups
1 qt 4 c
3 qt x
=
x = 12
9-3 Converting Customary Units
Convert 144 cups to gallons.
Check It Out: Example 2
Convert cups to gallons.
16x = 144
16 • x = 1 • 144
144 cups = 9 gallons.
1 gallon is 16 cups. Write a proportion. Use a variable for the value you are trying to find.
The cross products are equal.
Divide both sides by 16 to undo multiplication.
144 cups = gallons.
1 gal 16 c
x 144 c=
x = 9
9-3 Converting Customary Units
11 Understand the Problem
Additional Example 3: Problem Solving Application
The football goal posts are 30 feet tall. How many inches is this?
The answer will be the height of the goal posts in inches.
List the important information:
• The height of the goal posts are 30 feet tall.
9-3 Converting Customary Units
Make a table from the information to show the number of inches in 1, 2, and 3 feet. Then find the number of inches in n feet.
22 Make a Plan
Additional Example 3 Continued
9-3 Converting Customary Units
30 • 12 = 360 so, the goal posts are 360 inches tall.
Additional Example 3 Continued
Solve33
12nn363242121
InchesFeet Look for a Pattern.
1 • 12 = 12
2 • 12 = 24
3 • 12 = 36
n • 12 = 12n
9-3 Converting Customary Units
Round 12 to 10. Then multiply by 30.
Additional Example 3 Continued
44 Look Back
30 • 10 = 300
The answer is reasonable because 360 is close to 300.
9-3 Converting Customary Units
11 Understand the Problem
Check It Out: Example 3
The soccer field is 110 yards long. How many inches is this?
The answer will be the length of the soccer field in inches.
List the important information:
• The soccer field is 110 yards long.
9-3 Converting Customary Units
Make a table from the information to show the number of inches in 1, 2, and 3 yard. Then find the number of inches in n yards.
22 Make a Plan
Check It Out: Example 3 Continued
9-3 Converting Customary Units
110 • 36 = 3,960 so, the soccer field is 3,960 inches long.
Check It Out: Example 3 Continued
Solve33
36nn1083722361
InchesYard Look for a Pattern.
1 • 36 = 36
2 • 36 = 72
3 • 36 = 108
n • 36 = 36n
9-3 Converting Customary Units
Round 110 to 100. Then multiply by 36.
Check It Out: Example 3 Continued
44 Look Back
36 • 100 = 3,600
The answer is reasonable because 3,960 is close to 3,600.
9-3 Converting Customary Units
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
9-3 Converting Customary Units
Lesson Quiz
1. Convert 5 yards to inches.
2. Convert 16 tons to pounds.
3. Convert 11 quarts to cups.
4. A project requires 288 inches of tape. How
many yards is this?
32,000 pounds
180 inches
44 cups
8 yards
9-3 Converting Customary Units
1. Which of the following represents 7 yards in inches?
A. 252 in. B. 245 in.
C. 238 in. D. 231 in.
Lesson Quiz for Student Response Systems
9-3 Converting Customary Units
2. Which of the following represents 12 tons in pounds?
A. 12,000 pounds B. 36,000 pounds
C. 24,000 pounds D. 40,000 pounds
Lesson Quiz for Student Response Systems
9-3 Converting Customary Units
3. Which of the following represents 14 quarts in cups?
A. 196 cups B. 112 cups
C. 84 cups D. 56 cups
Lesson Quiz for Student Response Systems
9-3 Converting Customary Units
4. An electrician requires 324 inches of electrical wire. How many yards is this?
A. 7 yards B. 8 yards
C. 9 yards D. 10 yards
Lesson Quiz for Student Response Systems