1. ALGEBRA READINESS LESSON 6-3 Warm Up Lesson 6-3 Warm-Up

2. ALGEBRA READINESS LESSON 6-3 Warm Up Lesson 6-3 Warm-Up

3. ALGEBRA READINESS “Dimensional Analysis” (6-3) What is a “unit analysis”? How do you use dimensional analysis to solve conversion problems in which you need to change the units in a rate? unit analysis (also called “dimensional analysis”): the process of changing units using conversion factors (unit rates in the form of fractions that include both the rate in the problem and the desired rate you want to “convert”, or change, to) To use dimensional analysis, start with the units. Multiply the given rate by conversion fractions in which the undesired units cancel out so that only the desired units are left. To change the numerator unit if a rate, multiply by a conversion factor in which the new units are on top and the old units are on the bottom. To change the denominator unit of a rate, multiply by a conversion factor in which new units are on the bottom and the old units are on the top. Example: To change hours to minutes, you can multiply the number of hours by the “conversion fraction” as in: 3 hours = x = = 180 minutes Example: To change minutes to hours, you can multiply the number of hours by the “conversion fraction” as in: 300 minutes = x = 5 hours 3 hours 1 60 minutes 1 hour 180 minutes 1 300 minutes 1 1 hour 60 minutes 1 hour 60 minutes

4. ALGEBRA READINESS Convert 0.7 mi to feet. There are 3,696 feet in 0.7 miles. = 3,696 ft Simplify. Because 5,280 ft = 1 mi, use the conversion factor. 5,280 ft 1 mi 0.7 mi = Multiply by the conversion factor and divide the common units. Dimensional Analysis LESSON 6-3 Additional Examples 0.7 mi 1 5,280 ft 1 mi 0.7 5,280 ft 1 =

5. ALGEBRA READINESS A wilderness group completes a 15,000-meter hike in 5.2 hours. Find the group’s rate in meters per minute. Write the rate and multiply by the conversion factor. 15,000 m 5.2 h = 15,000 m 5.2 h 1h 60 min = 15,000 m 5.2 h 1h 60 min Divide the common units. ≈ 48.1 meters each minute Simplify. Dimensional Analysis LESSON 6-3 Additional Examples = 15,000 m 310 min Multiply across.

6. ALGEBRA READINESS The director of a political campaign has a project that will take 90 volunteer-hours. The project must be completed in 6 hours. How many volunteers will the director need? To eliminate “hours” from “volunteer-hours”, divide these units. The project requires 15 volunteers. Since the question asked for the number of volunteers, the answer must be volunteers, which means the “hours” in “volunteer-hours” needs to be eliminated. Dimensional Analysis LESSON 6-3 Additional Examples 90 volunteer-hours 6 hours 90 volunteer 6

7. ALGEBRA READINESS The fastest recorded speed for an eastern gray kangaroo is 40 mi per hour. What is the kangaroo’s speed in feet per second? The kangaroo’s speed is about 58.7 feet per second. 40 mi. 1 h Dimensional Analysis LESSON 6-3 Additional Examples Multiply by conversion factors until you are left only with the desired units. 5280 ft 1 mi 1 h 60 min. 1 min 60 sec = 211,200 ft 3,600 sec = 58.6 ft 1 sec   3,600

8. ALGEBRA READINESS 1.Convert 0.75 hours to seconds. $150 per hour is how much per minute? 3. A downhill skier travels 2,640 feet in 2 minutes. Find the skier’s rate of travel in feet per second. 2,700 s $2.50 per min 22 ft/s 2. Dimensional Analysis LESSON 6-3 Lesson Quiz