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9-3 Converting Customary Units
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
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
Course 1
9-3 Converting Customary Units
48, 96, 144, 192, 240
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
Course 1
9-3 Converting Customary Units
Learn to convert customary units of measure.
Course 1
9-3 Converting Customary Units
You can use the information in the table below to convert one customary unit to another.
Course 1
9-3 Converting Customary Units
When you convert units of measure to another, you can multiply or divide by a conversion factor.
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 x
Think: yards to feet- 3 feet = 1 yd, so use .3 ft 1 yd
3 ft 1 yd
Course 1
9-3 Converting Customary Units
Write the unit you are converting to in the numerator and the unit you are converting from in the denominator.
Caution!
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 lbs = 5 tons
10,000 lbs x
Think: pounds to tons- 1 ton = 2,000 lbs, so
use . 1 ton s 2,000 lbs
1 ton 2,000 lbs
Course 1
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 x
Think: quarts to pints- 2 pints = 1 quart, so use
.
2 pt 1 qt
2 pt 1 qt
Course 1
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 x
Think: feet to miles- 1 mile = 5,280 feet, so
use . 1 mile 5,280 ft
1 mi s 5,280 ft
Course 1
9-3 Converting Customary Units
Another way to convert units is to use proportions.
Course 1
9-3 Converting Customary Units
A proportion shows that two ratios are equivalent. Use a conversion factor for one of the ratios.
Remember!
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.
Course 1
9-3 Converting Customary Units
3 qt = cups
1 qt 4 c
3 qt x
=
x = 12
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.
Course 1
9-3 Converting Customary Units
144 cups = gallons.
1 gal 16 c
x 144 c=
x = 9
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.
Course 1
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
Course 1
9-3 Converting Customary Units
30 • 12 = 360 so, the goal posts are 360 inches tall.
Additional Example 3 Continued
Course 1
9-3 Converting Customary Units
Solve33
Feet Inches
1 12
2 24
3 36
n 12n
Look for a Pattern.
1 • 12 = 12
2 • 12 = 24
3 • 12 = 36
n • 12 = 12n
Round 12 to 10. Then multiply by 30.
Additional Example 3 Continued
Course 1
9-3 Converting Customary Units
44 Look Back
30 • 10 = 300
The answer is reasonable because 360 is close to 300.
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.
Course 1
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
Course 1
9-3 Converting Customary Units
110 • 36 = 3,960 so, the soccer field is 3,960 inches long.
Check It Out: Example 3 Continued
Course 1
9-3 Converting Customary Units
Solve33
Yard Inches
1 36
2 72
3 108
n 36n
Look for a Pattern.
1 • 36 = 36
2 • 36 = 72
3 • 36 = 108
n • 36 = 36n
Round 110 to 100. Then multiply by 36.
Check It Out: Example 3 Continued
Course 1
9-3 Converting Customary Units
44 Look Back
36 • 100 = 3,600
The answer is reasonable because 3,960 is close to 3,600.
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
Insert Lesson Title Here
44 cups
8 yards
Course 1
9-3 Converting Customary Units
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