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PO D Write your own complex fraction that simplifies to ¼ PO D If Cole ran 12¼ miles on Sunday in 3½ hours, what what his speed in basic PO D After the first 15 games of the season, Stephen Curry had 31½ steals. How many steals per game did he have? advanced James Harden averages 27.2 points per game. A game is usually 48 minutes long. How many points per second does he average? 1-3 Convert Unit Rates Smaller Larger Smaller Larger 12 inches 1 foot 100 centimeters 1 meter 16 ounces 1 pound 1000 grams 1 kilogram 8 pints 1 gallon 1000 milliliters 1 liter 3 feet 1 yard 10 millimeters 1 centimeter 5,280 feet 1 mile 1000 milligrams 1 gram Each of these relationships in the tables can be written as a unit ratio. 12 inches 1 foot 16 ounces 1 pound 100 centimeters 1 meter 1-3 Convert Unit Rates Smaller Larger Smaller Larger 12 inches 1 foot 100 centimeters 1 meter 16 ounces 1 pound 1000 grams 1 kilogram 8 pints 1 gallon 1000 milliliters 1 liter 3 feet 1 yard 10 millimeters 1 centimeter 5,280 feet 1 mile 1000 milligrams 1 gram Each of these relationships in the tables can be written as a unit ratio. 12 inches 1 foot 16 ounces 1 pound 100 centimeters 1 meter You can convert one rate to an equivalent rate by multiplying by a unit ratio or its reciprocal. You must include units in your computation. The process of including units of measure as factors when you compute is called dimensional analysis. 10 ft 1s = 10 ft 1s × 12 in 1 ft = 10 × 12 in 1s×1 = 120 in. 1s Example 1.) A remote control car travels at a rate of 10 feet per second. How many inches per second is this? 10 ft 1s = 10 ft 1s = 10 ft 1s = = × 12 in 1 ft Use 1 foot = 12 inches. Multiply by × 12 in 1 ft Divide out common units 10 × 12 in 1s×1 120 in. 1s Simplify Simplify 12 in. 1 ft. 2.) A swordfish can swim at a rate of 60 miles per hour. How may feet per hour is this? 60 mi 1 hr × 5280 ft 1 mi 5280 ft. Multiply by 1 mi. × 5280 ft 1 mi Divide out common units = 60 mi 1 hr = 60 mi 1 hr = 60 × 5280 ft 1 hr × 1 Simplify = 316,800 ft 1 hr Simplify 3.) Marvin walks at a speed of 7 feet per second. How many feet per hour is this? 7 ft 1s = = 7 ft × 1s 7 ft × 1s 60 s × 1 min 60 s × 1 min 60 min 1h 60 min 1h 60 s Multiply by 1 min and Divide out common units = 7 × 60 × 60ft 1 ×1 × 1h Simplify = 25,200 ft 1 hr Simplify 60 min 1h 4.) A gull can fly at a speed of 22 miles per hour. About how many feet per hour can the gull fly? 22 mi 1h = = 22 mi × 1h 5280ft 1 mi 22 mi × 5280 ft 1h 1 mi 5280 ft Multiply by 1 mi Divide out common units = 22 × 5280ft 1h × 1 Simplify = 116,160 ft 1h Simplify 5.) An Amtrak train travels at 125 miles per hour. Convert the speed to miles per minute. Round to the nearest tenth. 125 mi 1h = 125 mi × 1h = 1h 60 min 125 mi × 1h 1h 60 min 1h Multiply by 60 min Divide out common units = 125 mi × 1 1 × 60 min Simplify = 2.1 mi 1 min Simplify