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