which can be set up as Upon division, you should get the quotient 32.6 miles per hour, or 32.6 mi/hr, or 32.6 mph.

Transcription

1 133 CH 23 PER Many phrases in math, science, and business have the word per in them. In fact, a large number of all the formulas you ll ever see are based on the word per. The beauty of this word is that it always means divide. Moreover, I ll let you in on a little secret if you promise not to tell anyone, especially your science teacher: You can solve just about any per problem without having any idea what you re doing! You don t even have to know what any of the terms mean -- you can still get the right answer. How about that? Per always means DIVIDE EXAMPLES 1. Miles per hour: This one you probably already know. Miles per hour is speed (or rate), so if a car traveled 75 miles in 2.3 hours, then the speed was Speed = miles per hour = miles hours = 75 mi 2.3 hrs, which can be set up as Upon division, you should get the quotient 32.6 miles per hour, or 32.6 mi/hr, or 32.6 mph. 2. Perhaps you don t know what density or gram or cc means. Even so, if you know that density can be measured in grams per cc, you ve got a formula for density. For instance, if 18 cc s of a medicine has a mass of 13.5 grams, then its density is Density = grams per cc = grams cc = grams cc which can be set up as = 0.75 grams per cc, or 0.75 g/cc. = 13.5 grams 18 cc' s

2 Don t care about football? You can still calculate a running back s yards per carry by simply dividing yards by carries. For example, if a running back gains 123 yards in 15 carries, then the yards per carry is yards carries = 123 yds 15 carries = 8.2 yds/carry (The division setup would be ) 4. Frequency can be defined as cycles per second. Don t care for science? You can still work the following problem: If 36 cycles occurred in 48 seconds, what is the frequency? Frequency = cycles per second = cycles seconds = cycles seconds = second cycles = 48seconds 36 cycles = 0.75 cycles/sec (or 0.75 cps or 0.75 Hz) One cycle/sec is called one Hertz, in honor of Heinrich Hertz ( ), the first to demonstrate experimentally how electromagnetic waves move through space. This discovery lead directly to radio, television, and radar.

3 135 Homework 1. The snail crawled 66 feet in 3 sec. Find the snail s speed in ft per sec. 2. If density is measured in pounds per cubic feet, find the density of a liquid if 62.4 pounds of the liquid has a volume of 4 cubic feet. 3. Joe ran the football for 72 yards in 12 carries. How well did he do in yards per carry? 4. An electric wave had 6,000 cycles pass in 30 seconds. Find the frequency (cycles per second). 5. Pressure can be measured in pounds per square inch. Find the pressure if 200 pounds of force are pushing against 40 square inches. 6. The snail crawled 12 feet in 48 sec. Find the snail s speed in ft per sec. 7. If density is measured in pounds per cubic feet, find the density of a liquid if 62 pounds of the liquid has a volume of 124 cubic feet. 8. Joe ran the football for 72 yards in 48 carries. How well did he do in yards per carry? 9. An electric wave had 6 cycles pass in 30 seconds. Find the frequency (cycles per second). 10. The molarity of a solution is found by calculating moles per liter. Find the molarity of a solution if 20 liters of solution contains 140 moles of a substance. 11. Pressure can be measured in pounds per square inch. Find the pressure if 200 pounds of force are pushing against 150 square inches. 12. The molarity of a solution is found by calculating moles per liter. Find the molarity of a solution if 20 liters of solution contains 4 moles of a substance. 13. The miles per gallon that your car gets is referred to as its mileage. Find the mileage of a car that can go 865 miles on 20 gallons of gas.

4 Find the mileage (miles per gallon) of a space shuttle transport if the transport uses 200 gallons of gas to travel 60 miles. 15. The unit price of an item measured in pounds is simply its cost per pound. Find the unit price of 2.3 pounds of top sirloin if the total cost of the meat was $ The unit price can also be the price per single item. What is the unit price of a CD-recordable if a box containing 25 of them costs $21.25? 17. The most important characteristic of a stock is the price per share. Find the price per share if Millie bought 150 shares of ebay for a total of $9, One way to describe how a company s doing is to compute its earnings per share. This is much more useful for investment purposes than simply the total earnings. A company with earnings of $43,845 has 18,500 outstanding shares. Find the earning per share. 19. Tile is purchased by the square foot. If Sam bought 260 square feet of tile for a total cost of $1,508, find the price per square foot. 20. A large pipe is leaking so that 4,590 gallons have leaked over the last 20 minutes. Find the leak rate in gallons per minute. 21. Power can be defined as energy per time. Find the power in joules per second if 2,400 joules of energy were expended in 150 seconds. 22. The cholesterol level in your blood is measured in mg per dl (milligrams of cholesterol per deciliter of blood). Suppose a blood test measures 6,920 mg of cholesterol in 34.6 dl of blood. Find the cholesterol level. 23. Suppose a blood test measures 50 mg of cholesterol in 0.2 dl of blood. Find the cholesterol level. 24. The unit price of an item measured in pounds is simply its cost per pound. Find the unit price of 45 pounds of apples if the total cost of the apples was $9.

5 The most important characteristic of a stock is the price per share. Find the price per share if Millie bought 500 shares of ebay for a total of $ The worm consumed 22 grams of fiber in 44 hours. Find the consumption rate in grams per hour. 27. The Lions football team had 28 turnovers in 10 games. Find the average turnovers per game. 28. The Giants hit 12 home runs in 60 innings. Calculate their home runs per inning statistic. 29. The Dodgers hit 21 home runs in 105 innings. Compute their innings per home run statistic. 30. The area of the table is 12 square meters, and has 9 lumens shining on it. Find the light density in terms of lumens per square meter. 31. Power can be defined as energy per time. Find the power in joules per second if 24 joules of energy were expended in 30 seconds. 32. Find the charge per cubic centimeter if a region of space with a volume of 1,000 cubic centimeters has a total charge of 950 coulombs. Solutions ft/sec lb/cu ft 3. 6 yd/carry cycles/sec 5. 5 lb/sq in ft/sec lb/cu ft yd/carry cycles/sec moles/liter lb/sq in moles/liter mi/gal mi/gal 15. $4.80/lb

6 $0.85/CD 17. $62/share 18. $2.37/share 19. $5.80/sq ft gal/min joules/sec mg/dl mg/dl 24. $0.20/lb 25. $0.78/share g/hr turnovers/g hr/inning inn/hr lm/m joules/sec C/cm 3 What the mind of man can conceive and believe, it can achieve. Napoleon Hill