4 7 Dimensional Analysis Warm Up Problem of

4 -7 Dimensional Analysis Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

4 -7 Dimensional Analysis Warm Up Find each unit rate. 1. jump rope 192 times in 6 minutes 32 jumps/min 2. four pounds of bananas for $2. 36 $0. 59/lb 3. 16 anchor bolts for $18. 56 $1. 16/bolt 4. 288 movies on 9 shelves 32 movies/shelf

4 -7 Dimensional Analysis Problem of the Day The sum of four consecutive integers is 182. What are the four numbers? 44, 45, 46, and 47

4 -7 Dimensional Analysis Sunshine State Standards MA. 7. G. 4. 4 Compare, contrast, and convert units of measure between different measurement systems (US customary or metric (SI)), dimensions, and derived units to solve problems.

4 -7 Dimensional Analysis Vocabulary unit conversion factor

4 -7 Dimensional Analysis A unit conversion factor is a fraction in which the numerator and denominator represent the same quantity in different units.

4 -7 Dimensional Analysis Additional Example 1: Using Conversion Factors to Solve Problems The average American uses 580 pounds of paper year. Find this rate in pounds 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. 580 lb 1 yr = 1 yr 12 mo 580 lb 12 mo = 48. 3 lb per month Multiply the ratio by the conversion factor. yr lb lb = • Cancel yr units. yr mo mo Divide 580 by 12. The average American uses 48. 3 pounds of paper month.

4 -7 Dimensional Analysis Check It Out: Example 1 Sam drives his car 23, 000 miles per year. Find the number of miles he drives per month, to the nearest mile. The problem gives the ratio 23, 000 miles to 1 year and asks for an answer in miles per month. 23, 000 mi 1 yr 12 mo = 23, 000 mi 12 mo Multiply the ratio by the conversion factor. mi • yr = mi Cancel yr units. yr mo mo = 1916. 6 per month Divide 23, 000 by 12. Sam drives his car about 1917 miles per month.

4 -7 Dimensional Analysis Additional Example 2: Converting Between Metric and Customary Units One mile is about 1. 6 kilometers. What is the length in miles of a 10 kilometer race? Round to the nearest tenth of a miles kilometers 1 1. 6 = x 10 Write a proportion using 1 mi. = 1. 6 km. The cross products 1 · 10 = 1. 6 · x are equal. 10 = 1. 6 x ___ 1. 6 6. 25 = x Multiply. Divide each side by 1. 6. A 10 kilometer race is about 6. 3 miles.

4 -7 Dimensional Analysis Check It Out: Example 2 1 hour is equal to 60 minutes. What is the time in hours for a 165 minute movie? Round to the nearest hour minutes 1 60 x = 165 Write a proportion using 1 hour = 60 min The cross products 1 · 165 = 60 · x are equal. 165 = 60 x ___ 60 60 2. 75 = x Multiply. Divide each side by 60. A 165 minute movie is about 3 hours.

4 -7 Dimensional Analysis Additional Example 3: Application A tennis pro serves a ball that travels the length of the court, 78 feet, in 0. 75 second. How fast is the ball moving in feet per second? Check your answer for reasonableness.

4 -7 Dimensional Analysis Additional Example 3 Continued The ball’s speed is 104 ft/s. Convert ft/s to mi/h to see if the answer is reasonable. The ball’s average speed is 71 mi/h, which is a reasonable speed for a serve.

4 -7 Dimensional Analysis Check It Out: Example 3 A strobe lamp can be used to measure the 1 speed of an object. The lamp flashes every 100 of a second. A camera records the object moving 65 cm between flashes. How fast is the object moving in m/s? 65 cm 1 s 100 Use rate = distance. time

4 -7 Dimensional Analysis Check It Out: Example 3 Continued It may help to eliminate the fraction 65 cm = 100 • 65 cm 1 1 s 100 • s 100 = 6500 cm 1 s 1 first. 100 Multiply top and bottom by 100.

4 -7 Dimensional Analysis Check It Out: Example 3 Continued Now convert centimeters to meters. 6500 cm 1 s = 6500 cm • 1 m 100 cm 1 s 65 m = 6500 m = 1 s 100 s The object is traveling 65 m/s. Multiply by the conversion factor.

4 -7 Dimensional Analysis Lesson Quizzes Standard Lesson Quiz for Student Response Systems

4 -7 Dimensional Analysis Lesson Quiz Find the appropriate factor for each conversion. 1. 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? 29, 920 yd gal 2. One ounce is about 28. 3 grams. A box of cereal has a mass of 400 grams. What is the weight of the box in ounces? Round to the nearest tenth of an ounce. 14. 1 oz

4 -7 Dimensional Analysis Lesson Quiz Find the appropriate factor for each conversion. 3. A cheetah was timed running 200 yards in 6 seconds. What was the average speed in miles per hour? ≈ 68 mi/h

4 -7 Dimensional Analysis Lesson Quiz for Student Response Systems 1. A recipe for lemonade requires diluting the lemonade concentrate with 6 quarts of water. How many gallons of water are required to dilute the concentrate? A. 1 gallon B. 1. 5 gallons C. 2 gallons D. 2. 5 gallons

4 -7 Dimensional Analysis Lesson Quiz for Student Response Systems 2. There about 400 jelly beans in a pound. There are 2. 2 pounds in a kilogram. About how many grams does a jelly bean weigh? A. 0. 85 g B. 0. 98 g C. 1. 06 g D. 1. 14 g

4 -7 Dimensional Analysis Lesson Quiz for Student Response Systems 3. A sea horse swims at about 0. 01 miles per hour. What is the swim speed in inches per second? A. 10. 56 inches per second B. 10. 75 inches per second C. 11. 24 inches per second D. 11. 5 inches per second