Transcript 9-3

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