9-3 Converting Customary Units

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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

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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.

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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

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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

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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

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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

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9-3 Converting Customary Units

Another way to convert units is to use proportions.

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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.

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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.

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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.

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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

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9-3 Converting Customary Units

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

Additional Example 3 Continued

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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

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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.

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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

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9-3 Converting Customary Units

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

Check It Out: Example 3 Continued

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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

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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

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9-3 Converting Customary Units