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8-1 Converting Customary Units Learn to convert customary units of measure.

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8-1 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.

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8-1 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 Write the unit you are converting to in the numerator and the unit you are converting from in the denominator. Caution!

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8-1 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

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8-1 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

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8-1 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

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8-1 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!

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8-1 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

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8-1 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

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8-1 Converting Customary Units 1 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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8-1 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. 2 Make a Plan Additional Example 3 Continued

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8-1 Converting Customary Units 30 12 = 360 so, the goal posts are 360 inches tall. Additional Example 3 Continued Solve 3 12nn 363 242 121 InchesFeet Look for a Pattern. 1 12 = 12 2 12 = 24 3 12 = 36 n 12 = 12n

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8-1 Converting Customary Units Round 12 to 10. Then multiply by 30. Additional Example 3 Continued 4 Look Back 30 10 = 300 The answer is reasonable because 360 is close to 300.

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8-1 Converting Customary Units 1 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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8-1 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. 2 Make a Plan Check It Out: Example 3 Continued

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8-1 Converting Customary Units 110 36 = 3,960 so, the soccer field is 3,960 inches long. Check It Out: Example 3 Continued Solve 3 36nn 1083 722 361 InchesYard Look for a Pattern. 1 36 = 36 2 36 = 72 3 36 = 108 n 36 = 36n

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8-1 Converting Customary Units Round 110 to 100. Then multiply by 36. Check It Out: Example 3 Continued 4 Look Back 36 100 = 3,600 The answer is reasonable because 3,960 is close to 3,600.

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