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Chapter 6 mr. gonzalez


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  • 1. Percents and Their Applications in Business (p.166) CHAPTER 6
    • 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
  • 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. Understanding and Converting Percents
    • percent
      • A way of representing the parts 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%.
    • (p.166)
  • 5. Converting Percents to Decimals
    • (p.167)
  • 6. Converting Percents to Decimals Example 28% .28 13.4% .134 .065 6½% = 6.5% .0002 .02%
  • 7. Converting Decimals to Percents
    • (p.168)
  • 8. Converting Decimals to Percents Example 3.5 .34½ 350% .345 = 34.5% .935% 533% .00935 5.33
  • 9. Converting Percents to Fractions
    • (p.169)
  • 10. Converting Percents to Fractions Example
  • 11. Converting Percents to Fractions Example (cont’d)
  • 12. Converting Fractions to Percents
    • (p.170)
  • 13. Converting Fractions to Percents
  • 14. SECTION 2 (p.172)
  • 15. Using the Percentage Formula to Solve Business Problems
    • 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.
    • (p.172)
  • 16. Steps for Solving Percentage Problems
    • (p.173)
  • 17. The Magic Triangle
    • (p.173)
  • 18. Sample Percentage Problems
    • Maritza Torres owns 37% of a travel agency.
    • If the total worth of the business is $160,000, how much is Maritza’s share ?
  • 19. Sample Percentage Problems (cont’d)
    • What is the sales tax in a state where the tax on a purchase of $464 is $25.52?
  • 20. Sample Percentage Problems (cont’d)
    • The Daily Times reports that 28% of its advertising is for department stores.
    • If the department store advertising amounts to $46,200, what is the total advertising revenue of the newspaper?
  • 21. Sample Percentage Problems (cont’d)
    • Lisa Walden, 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?
  • 22. Sample Percentage Problems (cont’d)
    • A quality control process finds 17.2 defects for every 8,600 units of production.
    • What percent of the production is defective?
  • 23. Sample Percentage Problems (cont’d)
    • The Bentley Bobcats have won 80% of their basketball games. If they lost 4 games, how many games have been played?
    Won = 80% Lost = 20%
  • 24. Determining Rate of Increase or Decrease
    • (p.183)
  • 25. Rate of Increase or Decrease Example
    • 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?
  • 26. Rate of Increase or Decrease Example
    • 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?
  • 27. Determining the New Amount After a Percent Change
    • (p.173)
  • 28. Determining the New Amount After a Percent Change Example
    • 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?
  • 29. Determining the Original Amount Before a Percent Change
    • (p.188)
  • 30. Determining the Original Amount Before a Percent Change Example
    • Metro Motors sold 112 cars this month. If this is 40% better than last month, how many cars were sold last month?
  • 31. Determining the Original Amount Before a Percent Change Example (cont’d)
    • 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?
  • 32. Problems Involving Percentage Points
    • percentage points
      • A way of expressing a change from an original amount to a new amount, without using a percent sign.
    = Original amount of percentage points Change in percentage points Rate of change
  • 33. Problems Involving Percentage Points
    • 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?
  • 34. Problems Involving Percentage Points
    • 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?
  • 35. Chapter Review Problem 1
    • Solve the following by converting to a decimal:
  • 36. Chapter Review Problem 2
    • 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?
  • 37. Chapter Review Problem 3
    • If 453 runners out of 620 completed a marathon, what percent of the runners finished the race?
  • 38. Chapter Review Problem 4
    • By what percent is a 100-watt light bulb brighter than a 60-watt bulb?
  • 39. Chapter Review Problem 5
    • 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?