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# Module3

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### Module3

1. 1. Types of Strategies to SolvePercentage ProblemsBy: Kari Knisely
2. 2. What you will learn…When and how to use the following strategies:10% RulePercent ProportionPercent EquationPercent of Change EquationTic-Tac-Toe Table
3. 3. What you will need…Take notes as needed in order to familiarize yourself with thestrategies presented.PencilPaper
4. 4. 10% Rule When given an amount before a change (known as a whole or starting amount such as  Original price before increase/decrease  Subtotal before tax or tip  Total amount of questions possible on a test), then use 10% rule to estimate your answer
5. 5. 10% Rule Move the decimal 1 place to the left 10% of 40 = 4.0 10% of 32.6 = 3.26 10% of 2 = .2 10% of 5,345 = 534.5
6. 6. 10% Rule – Example 1 40% of 25 = ? 10% of 25 = 2.5 10% of 25 = 2.5 10 10% of 25 = 2.50 6.25 12.5 18.75 25 10% of 25 = 2.50% 25% 50% 75% 100% 40% of 25 = 10.0 40%
7. 7. 10% Rule –Example 2 30% of 30 = ? 10% of 30 = 3.0 9.0 10% of 30 = 3.00 7.5 15 22.5 30 10% of 30 = 3.00% 25% 50% 75% 100% 30% of 30 = 9.0 30%
8. 8. 10% Rule –Example 3 20% of 795 = ? 10% of 795 = 79.5 10% of 795 = 79.5 159 20% of 795 =159.00 198.75 397.5 596.25 7950% 25% 50% 75% 100% 20%
9. 9. Problems apply the 10% Rule to the Can you when you can apply 10% Rule of problems? these type Amount before a change
10. 10. Amount before change What was the subtotal?
11. 11. Problems apply the 10% Rule to the Can you when you can apply 10% Rule of problems? these type Amount before a change Amount after a change
12. 12. Amount after a change Subtotal \$9.00 How much total will you leave?
13. 13. Amount after a change How much total will you leave? 10% of 9.00 = 0.90Subtotal 5% of 9.00 = 0.45\$9.00 15% of 9.00 = 1.35 Subtotal \$ 9.00 Tip 1.35 Total \$10.35
14. 14. Problems apply the 10% Rule to the Can you when you can apply 10% Rule of problems? these type Amount before a change Amount after a change Percent after a change
15. 15. Percent after a change Subtotal \$8.59 Total \$12.00 (including tip, exclude sales tax)
16. 16. Percent after a change Subtotal \$8.59 100% Starting Price \$8.59 Total \$12.00 10% of \$8.59 = .859 = .86 (including tip only… ignore sales tax) 10% of \$8.59 = .859 = .86 120% \$10.31 10% of \$8.59 = .859 = .86 130% \$11.17 10% of \$8.59 = .859 = .86 140% \$12.03
17. 17. Can you apply apply the 10% Rule When you can the 10% Rule to these type of problems? Amount before a change Amount after a change Percent after a change Percent of change
18. 18. Percentage of Change Subtotal \$8.59 Total \$12.00 (including tip and 6% sales tax)
19. 19. Percentage of Change Subtotal \$8.59 Starting Price \$8.59 Total \$12.00 +10% of \$8.59 = .859 = .86 (including tip only… ignore sales tax) +10% of \$8.59 = .859 = .86 20% \$10.31 +10% of \$8.59 = .859 = .86 30% \$11.17 +10% of \$8.59 = .859 = .86 40% \$12.03
20. 20. Can you apply the 10% Rule to these type of problems? Amount before a change Amount after a change Percent after a change Percent of change Amount of change
21. 21. Amount of Change Subtotal \$8.59 Total \$12.00 (including tip and 6% sales tax)
22. 22. Percent Proportion Must be able to identify parts and whole to use Need to have 3 of 4 pieces of information
23. 23. Percent ProportionNonPercentage Part = % Percentage AmountAmount Whole 100 is % = 100 Non Percentage Percentage Amount of Amount
24. 24. Percent Proportion – Example 1 40% of 25 = ? is = % of 100 10 X = 400 6.25 12.5 18.75 25 25 100 100  X = 25  400% 25% 50% 75% 100% 100X = 1000 40% X = 10
25. 25. Percent Proportion – Example 2 30% of ? is 9 is = % of 100 9.00 7.5 15 22.5 30 9 = 30 X 1000% 25% 50% 75% 100% 100  9 = X  30 30% 900 = 30X 30 = X
26. 26. Percent Proportion – Example 3 159 is ? % of 795 is = % of 100 159 = X 1590 198.75 397.5 596.25 795 795 1000% 25% 50% 75% 100% 100  159 = 795  X 15900 = 795X 20% 20 = X
27. 27. Can you use the Percent Proportion to solve these type of problems? Amount before a change Amount after a change Percent after a change Percent of change Amount of change
28. 28. Amount before change 100 (20-X) = X  -20 2000 – 100X = -20X 2000 = 80X 25 = X What was the original price?
29. 29. Amount after a change\$30.00 100 X = 30  25 100X = 750 X = 7.50 \$30.00 + 7.50 What price will you pay? \$37.50
30. 30. Percent after a changeOriginal \$30.00Total \$25.00(after discount) 100 -5 = 30  -X -500 = -30X 16.6 = X 100% - 16.6% = 83.3%
31. 31. Percent of ChangeOriginal \$30.00Total \$25.00(after discount) 100 -5 = 30  -X -500 = -30X 16.6 = X
32. 32. Amount of ChangeOriginal \$30.0040% discount 100 X = 30  -40 100X = -1200 X = -12 \$12.00
33. 33. Percent Equation %  Whole = Part
34. 34. Can you use the Percent Equation to solve these type of problems? Amount before a change Amount after a change Percent after a change Percent of change Amount of change
35. 35. Amount before change %  Whole = Part .80  x = 42 .80x = 42 x = 52.5 Approx 53 questionsHow many questions were on the test?
36. 36. Amount after a change %  Whole = Part .80  42 = X 33.6 = X Approx 34 questionsHow many questions were correct?
37. 37. Percent after a change %  Whole = Part %  42 = 35 % = .83 83%What percent of the questions wereanswered correctly?
38. 38. Percentage of Change %  Whole = Part %  42 = 35 % = .83 100% - 83% = 17%What percent of the questions wereanswered incorrectly?
39. 39. Amount of Change %  Whole = Part .83  42 = x 34.86= x 42 – 34.86 = 7.14 Approx 7 questions How many questions were answered incorrectly?
40. 40. Percent of Change Equation – Example 1New – Old = Percent of Change Old (as a decimal)
41. 41. Can you use the Percent of Change Equation to solve these type of problems? Amount before a change Amount after a change Percent after a change Percent of change Amount of change
42. 42. Amount before change New – Old Percent of Old = Change 59.95 - X = .06 X 59.95 – X = .06X 59.95 = 1.06X \$56.56 = XWhat was the original price if purchased in FL?
43. 43. Amount after a change New – Old Percent of Old = Change X – 59.99 = .06 59.99 X – 59.95 = 3.60 X = \$63.55 What is the total price after tax?
44. 44. Percent after a change Original \$79.99 New – Old % of Total \$62.00 Old = Chg (after discount and sales tax) 62.00 – 79.99 = -0.2249 79.99 -0.2249 X 100 = -22.5% 100% + -22.5% = 77.5%
45. 45. Percentage of Change Original \$79.99 New – Old % of Total \$84.49 Old = Chg (after sales tax) 84.49 – 79.99 = .05625 79.99 .05625 X 100 5.63%*Sale was not in FL
46. 46. Amount of Change Original New – Old = Percent of \$79.99 Old Change X – 79.99 = .06 79.99 X – 79.99 = 4.80 X = 84.79 84.79 – 79.99 = \$4.80*FL Sales Tax is 6%
47. 47. Tic-Tac-ToeWhole/Original Start 100Change (+ or -) % + or - %Part of Original End
48. 48. Can you use the Tic-Tac-Toe strategy to solve these type of problems? Amount before a change Amount after a change Percent after a change Percent of change Amount of change
49. 49. Tic-Tac-Toe AMOUNT PERCENT Original startingWhole/Original Start amount before change 100 % Amount of Percent of %Change (+ or -) Change Change + or -Part of Original Ending Ending amount after percent after % End change change
50. 50. 40 32 -8 100 80 -20 Tic-Tac-Toe AMOUNT PERCENTWhole/Original Start \$40.00 100 %Change (+ or -) -\$8.00 -20 % + or -Part of Original \$32.00 80 % End
51. 51. 100 80 -20 40 32 -8 Tic-Tac-Toe AMOUNT PERCENTWhole/Original Start \$40.00 100 %Change (+ or -) -\$8.00 -20 % + or -Part of Original \$32.00 80 % End
52. 52. 40 100 40 100 -8 -2032 80 -8 -20 32 80 Tic-Tac-Toe AMOUNT PERCENTWhole/Original Start \$40.00 100 %Change (+ or -) -\$8.00 -20 % + or -Part of Original \$32.00 80 % End
53. 53. 32 80 -8 -20 32 8040 100 40 100 -8 -20 Tic-Tac-Toe AMOUNT PERCENTWhole/Original Start \$40.00 100 %Change (+ or -) -\$8.00 -20 % + or -Part of Original \$32.00 80 % End
54. 54. -20 100 -20 80 -8 X X=40 -8 X X=32 Tic-Tac-Toe AMOUNT PERCENTWhole/Original Start \$40.00 100 %Change (+ or -) -\$8.00 -20 % + or -Part of Original \$32.00 80 % End
55. 55. 40 32 40 -8100 X X=80 100 X X=-20 Tic-Tac-Toe AMOUNT PERCENTWhole/Original Start \$40.00 100 %Change (+ or -) -\$8.00 -20 % + or -Part of Original \$32.00 80 % End
56. 56. X 15 118X = 1500100 118 X = 12.71 Amount before change What was the subtotal? ? 12.71 +2.29 +18 \$15.00 118
57. 57. 9 x 100X = 1035100 115 X = 10.35 Amount after a change Subtotal How much total will you leave? \$9.00 \$9.00 +1.35 +15 115 ? \$10.35
58. 58. 8.59 12 8.59X = 1200100 X X = 139.70 Percent after a change Subtotal \$8.59 Total \$12.00 (including tip ONLY) \$8.59 +3.41 +39.7 \$12.00 139.70 ?
59. 59. 8.59 3.41 8.59X = 341100 X X = 39.70 Percentage of Change Subtotal \$8.59 Total \$12.00 (including tip ONLY) \$8.59 +3.41 +39.70 ? \$12.00 139.7
60. 60. 12.00 – 8.59= 3.41 Amount of Change Subtotal \$8.59 Total \$12.00 (including tip ONLY) \$8.59 +3.41 ? \$12.00
61. 61. What you learned…When and how to use the following strategies:10% RulePercent ProportionPercent EquationPercent of Change EquationTic-Tac-Toe Table