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Pre-Algebra

Learn to use one or more conversion factors to solve rate problems. 7-3. Analyze Units. Pre-Algebra. 7-3. Analyze Units. Pre-Algebra.

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Pre-Algebra

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  1. Learn to use one or more conversion factors to solve rate problems. 7-3 Analyze Units Pre-Algebra

  2. 7-3 Analyze Units Pre-Algebra You can measure the speed of an object by using a strobe lamp and a camera in a dark room. Each time the lamp flashes, the camera records the object’s position. Problems often require dimensional analysis, also called unit analysis, to convert from one unit to another unit.

  3. 1 ft 12 in. 7-3 Analyze Units Pre-Algebra To convert units, multiply by one or more ratios of equal quantities called conversion factors. For example, to convert inches to feet you would use the ratio below as a conversion factor.

  4. Helpful Hint 7-3 Analyze Units • The conversion factor • must introduce the unit desired in the answer and • must cancel the original unit so that the unit desired is all that remains. Pre-Algebra

  5. There are 3 feet in 1 yard. To convert feet to yards, multiply the number of feet by . There are 16 ounces in 1 pound. To convert pounds to ounces, multiply the number of pounds by . 7-3 Analyze Units 1 yd 3 ft 16 oz 1 lb Pre-Algebra Example 1: Finding Conversion Factors Find the appropriate factor for each conversion. • A. feet to yards • B. pounds to ounces

  6. 580 lb 1 yr = 48.3 lb per month 580 lb 12 mo 1 yr 12 mo 7-3 Analyze Units = Pre-Algebra Example 2: Using Conversion Factors to Solve Problems The average American uses 580 pounds of paper per year. Find the number of pounds of paper the average American uses per month, to the nearest tenth. The problem gives the ratio 580 pounds to 1 year and asks for an answer in pounds per month. Multiply the ratio by the conversion factor Cancel yr units. Divide 580 by 12.

  7. The average American uses 48.3 pounds of paper per month. 7-3 Analyze Units Pre-Algebra Example 2 Continued The average American uses 580 pounds of paper per year. Find the number of pounds of paper the average American uses per month, to the nearest tenth.

  8. 23,000 mi 1 yr 1 yr 12 mo = 1916.6 per month 23,000 mi 12 mo 7-3 Analyze Units = Pre-Algebra Try This: Example 2 Sam drives his car 23,000 miles per year. Find the number of miles he drives per month. The problem gives the ratio 23,000 miles to 1 year and asks for an answer in miles per month. Multiply the ratio by the conversion factor Cancel yr units. Divide 23,000 by 12. Sam drives his car about 1917 miles per month.

  9. 1 h 60 min 7-3 Analyze Units Pre-Algebra Example 3: Problem Solving Application A car traveled 60 miles on a road in 2 hours. How many feet per second was the car traveling? Understanding The Problem The problem is stated in units of miles and hours. The question asks for the answer in units of feet and seconds. You will need to use several conversion factors. List the important information: 5280 ft 1 mi • Feet to miles • Hours to minutes 1 min 60 s • Minutes to seconds

  10. 60 min 1 h 1 h 60 min 1 min 60 s 7-3 Analyze Units hours to minutes minutes to seconds Pre-Algebra Solve First, convert 60 miles into feet. 5,280 ft 1 mi 316,800 ft = 60 mi • Second, convert 2 hours into seconds. 60 sec 1 min 2 hours • = 7,200 sec • Then simplify, 316,800 ft 7,200 sec 44 ft 1 sec =

  11. 60 • 5280 ft • 1 2 • 1 • 3600 s 316,800 ft 7200 s ft mi ft s 1 h 3600 s 7-3 mi h 5280 ft 1 mi h s Analyze Units 60 mi 2 h = = Simplify. Only remains. • • • • Pre-Algebra Solve Do not include the numbers yet. Notice what happens to the units. Multiply. 44 ft 1 s The car was traveling 44 feet per second.

  12. 1 ft 12 in. 7-3 Analyze Units Pre-Algebra To convert units, multiply by one or more ratios of equal quantities called conversion factors. For example, to convert inches to feet you would use the ratio below as a conversion factor.

  13. Helpful Hint 7-3 Analyze Units • The conversion factor • must introduce the unit desired in the answer and • must cancel the original unit so that the unit desired is all that remains. Pre-Algebra

  14. There are 60 seconds in 1 minute. To convert minutes to seconds, multiply the number of minutes by . There are 24 hours in 1 day. To convert hours to days, multiply the number hours by . 7-3 Analyze Units 1 day 24 h 60 sec 1 min Pre-Algebra Try This: Example 1 Find the appropriate factor for each conversion. A. minutes to seconds B. hours to days

  15. 1 h 60 min 7-3 Analyze Units Pre-Algebra Try This: Example 3 A train traveled 180 miles on a railroad track in 4 hours. How many feet per second was the train traveling? Understand the Problem The problem is stated in units of miles and hours. The question asks for the answer in units of feet and seconds. You will need to use several conversion factors. List the important information: 5280 ft 1 mi • Feet to miles • Hours to minutes 1 min 60 s • Minutes to seconds

  16. 180 • 5280 ft • 1 4 • 1 • 3600 s 950,400 ft 14,400 s ft mi ft s 1 h 3600 s 7-3 mi h 5280 ft 1 mi h s Analyze Units 180 mi 4 h = = Simplify. Only remains. • • • • Pre-Algebra Solve Do not include the numbers yet. Notice what happens to the units. Multiply. 66 ft 1 s The train was traveling 66 feet per second.

  17. A strobe lamp can be used to measure the speed of an object. The lamp flashes every of a second. A camera records the object moving 52 cm between flashes. How fast is the object moving in m/s? 1 100 distance . time 7-3 Analyze Units Use rate = Pre-Algebra Example 4: Physical Science Application

  18. 52 m 1 s 1 m 100 cm 52 cm .01 s 7-3 Analyze Units = = • Pre-Algebra Example 4 Continued Now convert centimeters to meters. 52 cm .01 s Multiply by the conversion factor. The object is traveling 52 m/s.

  19. 1 km 1000 m 5 nautical mi 1 h m nautical mi 1852 m 1 nautical mi 9.26 km 1 h 5 • 1852 • 1 km 1 h • 1 • 1000 9260 km 1000 h km h km m 7-3 nautical mi h Analyze Units • = = = • • • Set up the units to obtain in your answer. Pre-Algebra Example 5: Transportation Application The rate 1 knot equals 1 nautical mile per hour. One nautical mile is 1852 meters. What is the speed in kilometers per hour of a ship traveling at 5 knots? 5 knots = 5 nautical mi/h Examine the units. The ship is traveling 9.26 km/h.

  20. 1 ft 12 in. 7-3 Analyze Units Pre-Algebra To convert units, multiply by one or more ratios of equal quantities called conversion factors. For example, to convert inches to feet you would use the ratio below as a conversion factor.

  21. Helpful Hint 7-3 Analyze Units • The conversion factor • must introduce the unit desired in the answer and • must cancel the original unit so that the unit desired is all that remains. Pre-Algebra

  22. A strobe lamp can be used to measure the speed of an object. The lamp flashes every of a second. A camera records the object moving 65 cm between flashes. How fast is the object moving in m/s? 1 100 distance . time 7-3 Analyze Units Use rate = Pre-Algebra Try This: Example 4

  23. 65 m 1 s 1 m 100 cm 65 cm .01 s 7-3 Analyze Units = = • Pre-Algebra Try This: Example 4 Continued Now convert centimeters to meters. 65 cm .01 s Multiply by the conversion factor. The object is traveling 65 m/s.

  24. 1 km 1000 m 9 nautical mi 1 h m nautical mi 1852 m 1 nautical mi 16.67 km 1 h 16,668 km 1000 h 9 • 1852 • 1 km 1 h • 1 • 1000 km h km m 7-3 nautical mi h Analyze Units • = = ≈ • • • Set up the units to obtain in your answer. Pre-Algebra Try This: Example 5 The rate 1 knot equals 1 nautical mile per hour. One nautical mile is 1852 meters. What is the speed in kilometers per hour of a ship traveling at 9 knots? 9 knots = 9 nautical mi/h Examine the units. The ship is traveling about 16.67 km/h.

  25. A strobe lamp can be used to measure the speed of an object. The lamp flashes every of a second. A camera records the object moving 52 cm between flashes. How fast is the object moving in m/s? 1 100 distance . time 7-3 Analyze Units Use rate = Pre-Algebra Example 4: Physical Science Application

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