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

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

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 minutes 1 1 hour 60 minutes 1 hour 60 minutes

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 = 0.7 mi 1 5,280 ft 1 mi Multiply by the conversion factor and divide the common units. Dimensional Analysis LESSON 6-3 Additional Examples

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 m / min Simplify. Write the correct units. Dimensional Analysis LESSON 6-3 Additional Examples

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? 90 ÷ 6 = 15 Divide the volunteer-hours by the number of hours. The project requires 15 volunteers. volunteer hours hours = volunteers Divide the common units and simplify. The question asked for the number of volunteers, so the answer is reasonable. Check for Reasonableness Use dimensional analysis to check the units of your answer. Dimensional Analysis LESSON 6-3 Additional Examples

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 ft/s. 40 mi. 1 h 40 mi 1 h 5280 ft 1 mi 1 h 60 min Dimensional Analysis LESSON 6-3 Additional Examples Use appropriate conversion factors 5280 ft 1 mi 40 mi 1 h 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

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