MA 111 Review for Exam 1 Exam 1 given in class on Tuesday February 9 will cover Using Numbers and Quantities and Percent and Percent Change discussed in Sections 1 and 2 of the text Can you work each homework worksheet and quiz problem correctly and quickly providing explanations and justifications without looking at the text or your notes Have you carefully studied the material in the text You should be familiar with the following key ideas Understand the difference between number and quantity Know how to convert units e g miles hour to feet sec Know how to compare quantities with ratios and with percents Know how to understand or make better sense of very large or very small quantities Understand the importance of correct units Understand what percent means Know what the base of a percent is and be able to identify the base of a percent in context Be able to find different variables in a percentage calculation e g use the base and the result to find the percent Understand how changes in numbers can be measured by percents percent change Know how to increase or decrease a number by a percentage and how to reverse this process Understand the difference between 1 change 2 percent change 3 change in percent percentage points and 4 percent change of percent Be able to interpret a short passage and analyze the given information about numbers quantities percents and percent change 1 Practice Problems 1 I enjoy riding my recumbent bicycle at 12 miles per hour What is my speed in yards per minute 12 miles 5280 feet 1 yard 1 hour 352 feet 1 hour 1 mile 3 feet 60 minutes 1 minute 2 If light can travel 186 000 miles per second how many miles can it travel in one year Assume one year has 365 25 days 186 000 miles 60 seconds 60 minutes 24 hours 365 25 days 3 87 trillion miles 1 second 1 minute 1 hour 1 day 1 year 1 year 3 Compare the numbers 23 9 billion and 4 57 trillion as a ratio and as a percent Your answer should be in the form of complete sentences 4 57 trillion is about 191 times as large as 23 9 billion or 4 57 trillion is about 1 19100 of 23 9 billion 23 9 billion is about 191 of 4 57 trillion or 23 9 billion is about 0 52 of 4 57 trillion 4 Find an effective way to make sense of the size of Obama s proposed 3 8 trillion federal budget Examples Using the estimate that the world s population is about 6 67 billion with 3 8 trillion you could give each person on earth about 570 Using the estimate that the U S population is about 312 million each person s share of the debt in this country is about 12 000 5 Find an effective way to make sense of the size of a water molecule 0 2 nanometers which equals 0 0000000002 meters Example Using the estimate of a human hair being 0 00002 meters wide it would take about 100 000 water molecules to achieve the width of one hair 6 Express each of the following percentages as a decimal a 43 0 43 b 1 5 015 2 c 250 2 5 d 0 13 0013 7 If your score on a test was 62 points out of 70 express the score as a percentage 62 70 P 100 so P 62 70 100 89 8 What is 37 of 56 A 56 37 100 so A 37 100 56 20 72 9 78 is what percent of 52 78 52 P 100 so P 78 52 100 150 10 123 is 17 of what 123 N 17 100 so N 123 100 17 723 5 11 Out of a class of 35 students 28 students passed the midterm exam What percentage of the class failed the midterm If 28 students passed then 7 students failed 7 35 P 100 so P 7 35 100 20 12 If your income in one year is 65000 and you pay 10000 in income tax what is the tax rate 10000 65000 P 100 10000 65000 so P 100 15 4 13 If you buy a book that costs 19 95 and the sales tax is 6 what amount do you owe A 19 95 6 100 so A 6 100 19 95 1 20 14 If you read that the income tax is 230 per 1000 in income what is the tax rate as a percent 230 1000 P 100 so P 230 1000 100 23 15 Refer to the previous problem At that tax rate if you owed 34500 in income tax how much was your income 34500 N 23 100 so N 34500 100 23 150 000 3 16 In 2000 tuition at UK was 6550 In 2001 tuition increased by 7 How much was tuition at UK in 2001 Use B A 1 P 100 Here B 6550 1 7 100 7008 50 17 A computer that usually sells for 830 is on sale for 15 off How much does the computer cost Use B A 1 P 100 Here B 830 1 15 100 705 50 18 One year ago a gallon of gas sold for 2 82 Now the price of a gallon of gas is 2 63 By what percent has the price decreased over the past year 100 Here P Use P B A A by about 6 74 2 63 2 82 2 82 100 6 74 So the price has decreased 19 The population of Pleasantville this year is 5 900 This is a 3 increase over last year s population What was the size of the population of Pleasantville last year Use B A 1 P 100 Here 5900 A 1 3 100 so A 5900 1 03 5728 20 a If 300 is decreased by 5 what is the result P 5 Here B 300 1 100 285 Use B A 1 100 b If 300 is decreased by 15 and then the result is increased by 10 what is the final result 15 15 First use B A 1 100 Here B 300 1 100 255 So if 300 is decreased P by 15 the result is 255 Now increase 255 by 10 using B A 1 100 Here 10 B 255 1 100 280 5 15 Alternatively you can combine the two operations and calculate 300 1 100 1 10 280 5 100 c If a number is decreased by 15 and then the result is increased by 10 resulting in a final value of 300 what was the initial number P Longer way First reverse the increase of 10 using B A 1 100 Here 10 300 300 A 1 100 so A 1 1 272 7 Next reverse the decrease of 15 using 15 P Here 272 7 A 1 100 so A 272 7 320 8 B A 1 100 0 85 Shorter way Combining the two operations starting with the initial unknown 15 10 300 amount …