1. 7e Contemporary Mathematics FOR BUSINESS AND CONSUMERS Brechner PowerPoint Presentation by Domenic Tavella, MBA Percents and Their Applications in Business ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 1

2. 7e PERFORMANCE OBJECTIVES Section I Understanding and Converting Percents 6-1:Converting percents to decimals and decimals to percents 6-2:Converting percents to fractions and fractions to percents Section II Using the Percentage Formula to Solve Business Problems 6-3:Solving for the portion 6-4:Solving for the rate 6-5:Solving for the base Section III Solving Other Business Problems Involving Percents 6-6:Determining rate of increase or decrease 6-7:Determining amounts in increase or decrease situations 6-8:Understanding and solving problems involving percentage points 2 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

3. 7e Understanding and Converting Percents 3 percent A way of representing the part of a whole. Percent means “per hundred” or “parts per hundred.” percent sign The symbol, %, used to represent percents. For example, 1 percent would be written 1%. ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

4. 7e STEPS 4 STEP 1 Remove the percentage sign. STEP 2 Divide by 100. Note: If the percent is a fraction, such as 3/8% or a mixed number such as 4 ¾ %, change the fraction to a decimal; then follow Steps 1 and 2 above. 3/8% =.375% =.00375 4 ¾% = 4.75% =.0475 Note:If the percent is a fraction such as 2/3%, which converts to a repeating decimal,.66666, round the decimal to hundredths,.67; then follow Steps 1 and 2 above. 2/3% =.67% =.0067 FOR CONVERTING A PERCENT TO A DECIMAL ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

5. 7e Converting Percents to Decimals Example 5 37% 12.5% 7 ¼ % = 7.25%.04% ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part..37.125.0725.0004

6. 7e STEPS 6 STEP 1 Multiply by 100. STEP 2 Write a percent sign after the number. STEP 3 If there are fractions involved, such as ¾, convert them to decimals first; then proceed with Steps 1 and 2 above. ¾ =.75 = 75% FOR CONVERTING A DECIMAL OR WHOLE NUMBER TO A PERCENT ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

7. 7e Converting Decimals to Percents Example 7 2.9.83½ =.835.00827 6.24 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 290% 83.5%.827% 624%

8. 7e STEPS 8 STEP 1 Remove the percent sign. STEP 2 (If the percent is a whole number) Write a fraction with the percent as the numerator and 100 as the denominator. If that fraction is improper, change it to a mixed number. Reduce the fraction to lowest terms. or STEP 2 (If the percent is a fraction) Multiply the number by 1/100 and reduce to lowest terms. or STEP 2 (If the percent is a decimal) Convert it to a fraction and multiply by 1/100. Reduce to lowest terms. FOR CONVERTING PERCENTS TO FRACTIONS ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

9. 7e Converting Percents to Fractions Example 9 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 5% 37.5% 62 1 2 %.8% 1 20 3838 5 8 1 125

10. 7e Converting Percents to Fractions Example 10 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. continued

11. 7e STEPS 11 STEP 1 Change the fraction to a decimal by dividing the numerator by the denominator. STEP 2 Multiply by 100. (Move the decimal point two places to the right. Add zeros as needed.) STEP 3 Write a percent sign after the number. FOR CONVERTING FRACTIONS TO PERCENTS ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

12. 7e Converting Fractions to Percents Example 12 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

13. 7e Using the Percentage Formula to Solve Business Problems 13 base The variable of the percentage formula that represents 100%, or the whole thing.portion The variable of the percentage formula that represents a part of the base.rate The variable of the percentage formula that defines how much or what part the portion is of the base. The rate is the variable with the percent sign. ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

14. 7e STEPS 14 STEP 1 Identify the two knowns and the unknown. STEP 2 Choose the formula that solves for the unknown. STEP 3 Solve the equation by substituting the known values for the letters in the formula. Hint: By remembering one basic formula, P = R × B, you can derive the other two by using your knowledge of solving equations from Chapter 5. Because multiplication is indicated, we isolate the unknown by performing the inverse, or opposite, operation, division. FOR SOLVING PERCENTAGE PROBLEMS ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

15. 7e STEPS 15 FOR SOLVING PERCENTAGE PROBLEMS ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. continued

16. 7e Percentage Problem Example 16 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Maritza Torres owns 37% of the family restaurant. If the total worth of the business is $160,000.00. How much is Maritza’s share?

17. 7e Percentage Problem Example 17 What is the sales tax in a state where the tax on a purchase of $464 is $25.52? ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. continued

18. 7e Percentage Problem Example 18 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. continued The Daily Times reports that 28% of its advertising is for mobile telephone services. If the mobile telephone advertising amounts to $46,200, what is the total advertising revenue of the newspaper?

19. 7e Percentage Problem Example 19 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. continued Geri Carroll, a sales associate for a large company, successfully makes the sale on 40% of her sales presentations. If she made 25 presentations last week, how many sales did she make?

20. 7e Percentage Problem Example 20 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. continued A quality control process finds 17.2 defects for every 8,600 units of production. What percent of the production is defective?

21. 7e Percentage Problem Example 21 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. continued The Torryville Tigers have won 80% of their basketball games. If they lost 4 games, how many games have been played? Won = 80% Lost = 20%

22. 7e STEPS 22 STEP 1 Identify the original and the new amounts and find the difference between them. STEP 2 Using the rate formula R = P ÷ B, substitute the difference from Step 1 for the portion and the original amount for the base. STEP 3 Solve the equation for R. Remember, your answer will be in decimal form, which must be converted to a percent. FOR DETERMINING THE RATE OF INCREASE OR DECREASE ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

23. 7e Rate of Increase or Decrease Example 23 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Allied Plumbing sold 2,390 feet of 5/8-inch galvanized pipe in July. If 2,558 feet were sold in August, what is the percent increase in pipe footage sales?

24. 7e Rate of Increase or Decrease Example 24 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. continued The supermarket price of yellow onions dropped from $.59 per pound to $.45 per pound. What is the percent decrease in the price of onions?

25. 7e STEPS 25 STEP 1 In the formula Portion = Rate × Base, substitute the original amount, or starting point, for the base. STEP 2 If the rate change is an increase, add that rate to 100% to get the rate. or STEP 2 If the rate change is a decrease, subtract that rate from 100% to get the rate. STEP 3 Solve the equation for the portion. FOR DETERMINING THE NEW AMOUNT AFTER A PERCENT CHANGE ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

26. 7e Determining the New Amount After a Percent Change Example 26 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Economists predict that next year housing prices will drop by 4%. This year’s price for an average house is $110,000. What will the average price of a house be next year?

27. 7e STEPS 27 STEP 1 In the formula Base = Portion ÷ Rate, substitute the new amount for the portion. STEP 2 If the rate change is an increase, add that rate to 100% to get the rate. or STEP 2 If the rate change is a decrease, subtract that rate from 100% to get the rate. STEP 3 Solve the equation for the base. FOR DETERMINING THE ORIGINAL AMOUNT BEFORE A PERCENT CHANGE ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

28. 7e Determining the Original Amount Before a Percent Change Example 28 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. City Auto sold 112 cars this month. If this is 40% better than last month, how many cars were sold last month?

29. 7e Determining the Original Amount Before a Percent Change Example 29 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. continued The second shift of a factory produced 17,010 units. If this amount was 5 ½% less than the first shift, how many units were produced on the first shift?

30. 7e Problems Involving Percentage Points 30 percentage points A way of expressing a change from an original amount to a new amount without using a percentage sign. ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Rate of change = Change in percentage points Original amount of percentage points

31. 7e Problems Involving Percentage Points Example 31 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. After a vigorous promotion campaign, Erie Electronics increased its market share from 5.4% to 8.1%, a rise of 2.7 percentage points. What percent increase in market share does this represent?

32. 7e Problems Involving Percentage Points Example 32 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. continued The unemployment rate in Glen Haven dropped from 8.8% to 6.8% in the past year, a decrease of 2 percentage points. What percent decrease does this represent?

33. 7e CHAPTER REVIEW PROBLEM 1 33 Solve the following by converting to decimals: ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 89%.26% 9 ¾% = 9.75.89.0026.0975

34. 7e CHAPTER REVIEW PROBLEM 2 34 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. An ad read, “This week only, all merchandise 35% off!” If a television set normally sells for $349.95, what is the amount of the savings?

35. 7e CHAPTER REVIEW PROBLEM 3 35 If 453 runners out of 620 completed a marathon, what percent of runners finished the race? ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

36. 7e CHAPTER REVIEW PROBLEM 4 36 By what percent is a 100-watt light bulb brighter than a 60-watt light bulb? ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

37. 7e CHAPTER REVIEW PROBLEM 5 37 ©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. A pre-election survey shows that the popularity of a presidential candidate has increased from 26.5 percent to 31.3 percent of the electorate, an increase of 4.8 percentage points. What percent increase does this represent?