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# Chapter 6 mr. gonzalez

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### Chapter 6 mr. gonzalez

1. 1. Percents and Their Applications in Business (p.166) CHAPTER 6
2. 2. PERFORMANCE OBJECTIVES (p.166) <ul><li>Section I Understanding and Converting Percents </li></ul><ul><li>6-1: Converting percents to decimals and decimals to percents </li></ul><ul><li>6-2: Converting percents to fractions and fractions to percents </li></ul><ul><li>Section II Using the Percentage Formula to Solve Business Problems </li></ul><ul><li>6-3: Solving for the portion </li></ul><ul><li>6-4: Solving for the rate </li></ul><ul><li>6-5: Solving for the base </li></ul><ul><li>Section III Solving Other Business Problems Involving Percents </li></ul><ul><li>6-6: Determining rate of increase or decrease </li></ul><ul><li>6-7: Determining amounts in increase or decrease situations </li></ul><ul><li>6-8: Understanding and solving problems involving percentage points </li></ul>
3. 3. Understanding Equations The process of finding the numerical value of the unknown in an equation. Solve an Equation The knowns (constants) and unknowns (variables) of an equation. In the equation X + 7 = 10, the terms are X, 7, and 10. Terms The parts of an equation that are given. In equations, the knowns are constants (numbers), which are quantities having a fixed value. In the equation X + 7 = 10, 7 and 10 are the knowns or constants. Constants (Knowns) A mathematical operation or a quantity stated in symbolic form, not containing an equal sign. X + 7 is an expression. Expression A mathematical statement expressing a relationship of equality; usually written as a series of symbols that are separated into left and right sides and joined by an equal sign. X + 7 = 10 is an equation. Equation A mathematical representation of a fact, rule, principle, or other logical relation in which letters represent number quantities. Formula
4. 4. Understanding and Converting Percents <ul><li>percent </li></ul><ul><ul><li>A way of representing the parts of a whole. Percent means per hundred or parts per hundred. </li></ul></ul><ul><li>percent sign </li></ul><ul><ul><li>The symbol, %, used to represent percents. For example, 1 percent would be written 1%. </li></ul></ul><ul><li>(p.166) </li></ul>
5. 5. Converting Percents to Decimals <ul><li>(p.167) </li></ul>
6. 6. Converting Percents to Decimals Example 28% .28 13.4% .134 .065 6½% = 6.5% .0002 .02%
7. 7. Converting Decimals to Percents <ul><li>(p.168) </li></ul>
8. 8. Converting Decimals to Percents Example 3.5 .34½ 350% .345 = 34.5% .935% 533% .00935 5.33
9. 9. Converting Percents to Fractions <ul><li>(p.169) </li></ul>
10. 10. Converting Percents to Fractions Example
11. 11. Converting Percents to Fractions Example (cont’d)
12. 12. Converting Fractions to Percents <ul><li>(p.170) </li></ul>
13. 13. Converting Fractions to Percents
14. 14. SECTION 2 (p.172)
15. 15. Using the Percentage Formula to Solve Business Problems <ul><li>base </li></ul><ul><ul><li>The variable of the percentage formula that represents 100%, or the whole thing. </li></ul></ul><ul><li>portion </li></ul><ul><ul><li>The variable of the percentage formula that represents a part of the base. </li></ul></ul><ul><li>rate </li></ul><ul><ul><li>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. </li></ul></ul><ul><li>(p.172) </li></ul>
16. 16. Steps for Solving Percentage Problems <ul><li>(p.173) </li></ul>
17. 17. The Magic Triangle <ul><li>(p.173) </li></ul>
18. 18. Sample Percentage Problems <ul><li>Maritza Torres owns 37% of a travel agency. </li></ul><ul><li>If the total worth of the business is \$160,000, how much is Maritza’s share ? </li></ul>
19. 19. Sample Percentage Problems (cont’d) <ul><li>What is the sales tax in a state where the tax on a purchase of \$464 is \$25.52? </li></ul>
20. 20. Sample Percentage Problems (cont’d) <ul><li>The Daily Times reports that 28% of its advertising is for department stores. </li></ul><ul><li>If the department store advertising amounts to \$46,200, what is the total advertising revenue of the newspaper? </li></ul>
21. 21. Sample Percentage Problems (cont’d) <ul><li>Lisa Walden, a sales associate for a large company, successfully makes the sale on 40% of her sales presentations. </li></ul><ul><li>If she made 25 presentations last week, how many sales did she make? </li></ul>
22. 22. Sample Percentage Problems (cont’d) <ul><li>A quality control process finds 17.2 defects for every 8,600 units of production. </li></ul><ul><li>What percent of the production is defective? </li></ul>
23. 23. Sample Percentage Problems (cont’d) <ul><li>The Bentley Bobcats have won 80% of their basketball games. If they lost 4 games, how many games have been played? </li></ul>Won = 80% Lost = 20%
24. 24. Determining Rate of Increase or Decrease <ul><li>(p.183) </li></ul>
25. 25. Rate of Increase or Decrease Example <ul><li>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? </li></ul>
26. 26. Rate of Increase or Decrease Example <ul><li>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? </li></ul>
27. 27. Determining the New Amount After a Percent Change <ul><li>(p.173) </li></ul>
28. 28. Determining the New Amount After a Percent Change Example <ul><li>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? </li></ul>
29. 29. Determining the Original Amount Before a Percent Change <ul><li>(p.188) </li></ul>
30. 30. Determining the Original Amount Before a Percent Change Example <ul><li>Metro Motors sold 112 cars this month. If this is 40% better than last month, how many cars were sold last month? </li></ul>
31. 31. Determining the Original Amount Before a Percent Change Example (cont’d) <ul><li>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? </li></ul>
32. 32. Problems Involving Percentage Points <ul><li>percentage points </li></ul><ul><ul><li>A way of expressing a change from an original amount to a new amount, without using a percent sign. </li></ul></ul>= Original amount of percentage points Change in percentage points Rate of change
33. 33. Problems Involving Percentage Points <ul><li>After a vigorous promotion campaign, HiLo Mart increased its market share from 5.4% to 8.1%, a rise of 2.7 percentage points. What percent increase in sales does this represent? </li></ul>
34. 34. Problems Involving Percentage Points <ul><li>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? </li></ul>
35. 35. Chapter Review Problem 1 <ul><li>Solve the following by converting to a decimal: </li></ul>
36. 36. Chapter Review Problem 2 <ul><li>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? </li></ul>
37. 37. Chapter Review Problem 3 <ul><li>If 453 runners out of 620 completed a marathon, what percent of the runners finished the race? </li></ul>
38. 38. Chapter Review Problem 4 <ul><li>By what percent is a 100-watt light bulb brighter than a 60-watt bulb? </li></ul>
39. 39. Chapter Review Problem 5 <ul><li>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? </li></ul>