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Warm Up Find each unit rate. 1. Jump rope 192 times in 6 minutes

Warm Up Find each unit rate. 1. Jump rope 192 times in 6 minutes 2. Four pounds of bananas for $2.36 3. 16 anchor bolts for $18.56 4. 288 movies on 9 shelves. 32 jumps/min. $0.59/lb. $1.16/bolt. 32 movies/shelf. TB P. 224-228.

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Warm Up Find each unit rate. 1. Jump rope 192 times in 6 minutes

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  1. Warm Up Find each unit rate. 1. Jump rope 192 times in 6 minutes 2. Four pounds of bananas for $2.36 3. 16 anchor bolts for $18.56 4. 288 movies on 9 shelves 32 jumps/min $0.59/lb $1.16/bolt 32 movies/shelf

  2. TB P. 224-228 Learn to use one or more conversion factors to solve rate problems.

  3. Vocabulary conversion factor

  4. 1 ft 12 in. The process of converting from one unit to another is called dimensional analysis, or unit analysis. 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.

  5. 1 ft 12 in. Multiplying by a conversion factor is like multiplying by 1. 12 in. 12 in. 1 ft 1 ft = , or = 1

  6. Caution! Be sure to put the units you are converting to in the numerator and the units you are converting from in the denominator.

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

  8. The average American uses 48.3 pounds of paper per month. 580 lb 1 yr 1 yr 12 mo yr mo lb yr lb mo = • Cancel yr units. 580 lb 12 mo = = 48.3 lb per month Additional 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. Divide 580 by 12.

  9. Additional 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?

  10. 1 Understand the Problem 1 h 60 min 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

  11. Make a Plan 2 Multiply by each conversion factor separately, or simplify the problem and multiply by several conversion factors at once.

  12. 3 Solve 1 min 60 s hours to minutes minutes to seconds 1 h 3600 s 1 h 60 min = 30 mi 1 h 5280 ft 1 mi 1 h 3600 s • • 1 h 60 min First, convert 60 miles in 2 hours into a unit rate. 60 mi 2 h (60÷2) mi (2÷2) h 30 mi 1 h = = Create a single conversion factor to convert hours directly to seconds: 1 min 60 s hours to seconds = • Set up the conversion factors.

  13. 3 ft s ft mi mi h h s Simplify. Only remains. • • 1 h 3600 s 5280 ft 1 mi 30 mi 1 h • • 30 • 5280 ft • 1 1 • 1 • 3600 s 158,400 ft 3600 s = = Solve Continued 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.

  14. 4 Look Back A rate of 44 ft/s is less than 50 ft/s. A rate of 60 miles in 2 hours is 30 mi/h or 0.5 mi/min. Since 0.5 mi/min is less than 3000 ft/ 60 s or 50 ft/s and 44 ft/s is less than 50 ft/s, then 44 ft/s is a reasonable answer.

  15. 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 Use rate = 52 cm 1 100 s Additional Example 4: Physical Science Application

  16. 1 100 100 • 52 cm 1 100 = s 100 • 5200 cm 1 s 52 cm 1 100 = s Additional Example 4 Continued It may help to eliminate the fraction first. Multiply top and bottom by 100.

  17. 1 m 100 cm 5200 cm 1 s = • 5200 m 100 s 52 m 1 s = = Additional Example 4 Continued Now convert centimeters to meters. 5200 cm 1 s Multiply by the conversion factor. The object is traveling 52 m/s.

  18. Lesson Quiz Find the appropriate factor for each conversion. 1. kilograms to grams 2. pints to gallons 3. You drive 136 miles from your house to your aunt’s house at the lake. You use 8 gallons of gas. How many yards does your car get to the gallon? 4. A cheetah was timed running 200 yards in 6 seconds. What was the average speed in miles per hour? 1000 g kg 1 gal 8 pt 29,920 yd gal ≈ 68 mi/h

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