9-3 Converting Customary Units Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

9-3 Converting Customary Units

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


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


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


Learn to convert customary units of measure.


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.


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!


Additional Example 1B: Using a Conversion Factor

Convert 10,000 pounds to tons.


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


Check It Out: Example 1A

Convert 3 quarts to pints.


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


Check It Out: Example 1B

Convert 15,840 feet to miles.


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


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!


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


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


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.


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


30 • 12 = 360 so, the goal posts are 360 inches tall.


Solve33

12nn363242121

InchesFeet Look for a Pattern.

1 • 12 = 12

2 • 12 = 24

3 • 12 = 36

n • 12 = 12n


Round 12 to 10. Then multiply by 30.


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.


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


110 • 36 = 3,960 so, the soccer field is 3,960 inches long.


Solve33

36nn1083722361

InchesYard Look for a Pattern.

1 • 36 = 36

2 • 36 = 72

3 • 36 = 108

n • 36 = 36n


Round 110 to 100. Then multiply by 36.


44 Look Back

36 • 100 = 3,600

The answer is reasonable because 3,960 is close to 3,600.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


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


1. Which of the following represents 7 yards in inches?

A. 252 in. B. 245 in.

C. 238 in. D. 231 in.



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



3. Which of the following represents 14 quarts in cups?

A. 196 cups B. 112 cups

C. 84 cups D. 56 cups



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


Documents

9-3 Converting Customary Units Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes