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DIMENSIONAL ANALYSIS WARM-UP Four more than three times a number is one less than four times the number. What is the number? 4 3n 4n 1 3n 4n 1 4 n 5 n5 Dimensional Analysis • Dimensional Analysis is a procedure used to convert from one unit of measurement to a different unit of measurement. • To do dimensional analysis, you must understand what is meant by a unit fraction. Unit Fraction • A unit fraction is any fraction in which the numerator and denominator contain different units and the value of the fraction is 1. • The table on the next slide shows many unit fractions involving U.S. customary units. Examples of Unit Fractions Example: How many inches are in 5 feet? 12in. 5 ft x 60in. 1 ft. 8 oz is how many pounds? (Hint: 1 pound = 16 oz) 1 pound 8 1 8 oz x pounds 16oz 16 2 15 yards to feet 3 feet 15 yardsx (15x3) ft 45 ft 1 yard 4 feet to inches 12in 4 ft x 48in 1 ft 6 pints to cups (Hint: 1 pint = 2 cups) 2 cups 6 pts x 12cups 1 pt 42 inches to feet 1 ft 42 42in x 3.5 ft 12in 12 John drives on the interstate 60 miles per hour. How many feet per second is he traveling? mi 5280 ft 1hr 1 min 316800 ft 60 x x x 88 ft sec hr 1mi 60 min 60 sec 3600 sec Kim can scan 20 items per minute. How many can she scan in 15 seconds? • Find how many she can scan per second: 20 items 1Minute 20 1 items x sec Minute 60 sec 60 3 • Multiply by 15 seconds. 1 x15 5 items 3 Jared can work 54 math problems in 1 hour. How many problems can he work in 10 minutes? • Figure the amount per minute first: problem s 1hr 54 54 x hr 60Min 60 9 problem s Re ducesto Min 10 • Now multiply that amount by 10 minutes. 9 problems x10 Min 9 problems Min 10 A machine makes 360 gadgets every 24 hours. How many gadgets does it make every 20 minutes. • Find the # of gadgets per minute first: 360gadgets 1hour gadgets x .315 24hours 60 Min Min • Next, multiply by 20 minutes to get the # of gadgets. .315 gadgets x 20 Min 6.3 gadgets Min Perry’s car can travel an average of 22 miles on 1 gallon of gas. How many miles can his car travel on 1 quart of gas? (Hint: 1 gallon = 4 quarts) 22m iles 1 gallon 22 x m iles/ quart gallon 4 quarts 4 or 5.5 m iles quart