Module3
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This document discusses different strategies for solving percentage problems: 1) The 10% rule can be used when given an amount before a change to estimate answers by moving the decimal place one place left, representing 10% of the original amount. 2) Percent proportion uses parts and wholes to set up a ratio equation when given 3 of 4 key pieces of information. 3) The percent equation sets the percentage of the whole equal to the part to solve for unknown values. 4) The percent of change equation calculates the percentage change by subtracting the new amount from the old and dividing by the original value.
Module3
- 1. Types of Strategies to Solve Percentage Problems By: Kari Knisely
- 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. What you will need… Take notes as needed in order to familiarize yourself with the strategies presented. Pencil Paper
- 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. 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. 10% Rule – Example 1 40% of 25 = ? 10% of 25 = 2.5 10% of 25 = 2.5 10 10% of 25 = 2.5 0 6.25 12.5 18.75 25 10% of 25 = 2.5 0% 25% 50% 75% 100% 40% of 25 = 10.0 40%
- 7. 10% Rule –Example 2 30% of 30 = ? 10% of 30 = 3.0 9.0 10% of 30 = 3.0 0 7.5 15 22.5 30 10% of 30 = 3.0 0% 25% 50% 75% 100% 30% of 30 = 9.0 30%
- 8. 10% Rule –Example 3 20% of 795 = ? 10% of 795 = 79.5 10% of 795 = 79.5 159 20% of 795 =159.0 0 198.75 397.5 596.25 795 0% 25% 50% 75% 100% 20%
- 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. Amount before change What was the subtotal?
- 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. Amount after a change Subtotal $9.00 How much total will you leave?
- 13. Amount after a change How much total will you leave? 10% of 9.00 = 0.90 Subtotal 5% of 9.00 = 0.45 $9.00 15% of 9.00 = 1.35 Subtotal $ 9.00 Tip 1.35 Total $10.35
- 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. Percent after a change Subtotal $8.59 Total $12.00 (including tip, exclude sales tax)
- 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. 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. Percentage of Change Subtotal $8.59 Total $12.00 (including tip and 6% sales tax)
- 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. 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. Amount of Change Subtotal $8.59 Total $12.00 (including tip and 6% sales tax)
- 22. Percent Proportion Must be able to identify parts and whole to use Need to have 3 of 4 pieces of information
- 23. Percent Proportion Non Percentage Part = % Percentage Amount Amount Whole 100 is % = 100 Non Percentage Percentage Amount of Amount
- 24. Percent Proportion – Example 1 40% of 25 = ? is = % of 100 10 X = 40 0 6.25 12.5 18.75 25 25 100 100 X = 25 40 0% 25% 50% 75% 100% 100X = 1000 40% X = 10
- 25. Percent Proportion – Example 2 30% of ? is 9 is = % of 100 9.0 0 7.5 15 22.5 30 9 = 30 X 100 0% 25% 50% 75% 100% 100 9 = X 30 30% 900 = 30X 30 = X
- 26. Percent Proportion – Example 3 159 is ? % of 795 is = % of 100 159 = X 159 0 198.75 397.5 596.25 795 795 100 0% 25% 50% 75% 100% 100 159 = 795 X 15900 = 795X 20% 20 = X
- 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. Amount before change 100 (20-X) = X -20 2000 – 100X = -20X 2000 = 80X 25 = X What was the original price?
- 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. Percent after a change Original $30.00 Total $25.00 (after discount) 100 -5 = 30 -X -500 = -30X 16.6 = X 100% - 16.6% = 83.3%
- 31. Percent of Change Original $30.00 Total $25.00 (after discount) 100 -5 = 30 -X -500 = -30X 16.6 = X
- 32. Amount of Change Original $30.00 40% discount 100 X = 30 -40 100X = -1200 X = -12 $12.00
- 33. Percent Equation % Whole = Part
- 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. Amount before change % Whole = Part .80 x = 42 .80x = 42 x = 52.5 Approx 53 questions How many questions were on the test?
- 36. Amount after a change % Whole = Part .80 42 = X 33.6 = X Approx 34 questions How many questions were correct?
- 37. Percent after a change % Whole = Part % 42 = 35 % = .83 83% What percent of the questions were answered correctly?
- 38. Percentage of Change % Whole = Part % 42 = 35 % = .83 100% - 83% = 17% What percent of the questions were answered incorrectly?
- 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. Percent of Change Equation – Example 1 New – Old = Percent of Change Old (as a decimal)
- 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. Amount before change New – Old Percent of Old = Change 59.95 - X = .06 X 59.95 – X = .06X 59.95 = 1.06X $56.56 = X What was the original price if purchased in FL?
- 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. 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. 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. 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. Tic-Tac-Toe Whole/Original Start 100 Change (+ or -) % + or - % Part of Original End
- 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. Tic-Tac-Toe AMOUNT PERCENT Original starting Whole/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. 40 32 -8 100 80 -20 Tic-Tac-Toe AMOUNT PERCENT Whole/Original Start $40.00 100 % Change (+ or -) -$8.00 -20 % + or - Part of Original $32.00 80 % End
- 51. 100 80 -20 40 32 -8 Tic-Tac-Toe AMOUNT PERCENT Whole/Original Start $40.00 100 % Change (+ or -) -$8.00 -20 % + or - Part of Original $32.00 80 % End
- 52. 40 100 40 100 -8 -20 32 80 -8 -20 32 80 Tic-Tac-Toe AMOUNT PERCENT Whole/Original Start $40.00 100 % Change (+ or -) -$8.00 -20 % + or - Part of Original $32.00 80 % End
- 53. 32 80 -8 -20 32 80 40 100 40 100 -8 -20 Tic-Tac-Toe AMOUNT PERCENT Whole/Original Start $40.00 100 % Change (+ or -) -$8.00 -20 % + or - Part of Original $32.00 80 % End
- 54. -20 100 -20 80 -8 X X=40 -8 X X=32 Tic-Tac-Toe AMOUNT PERCENT Whole/Original Start $40.00 100 % Change (+ or -) -$8.00 -20 % + or - Part of Original $32.00 80 % End
- 55. 40 32 40 -8 100 X X=80 100 X X=-20 Tic-Tac-Toe AMOUNT PERCENT Whole/Original Start $40.00 100 % Change (+ or -) -$8.00 -20 % + or - Part of Original $32.00 80 % End
- 56. X 15 118X = 1500 100 118 X = 12.71 Amount before change What was the subtotal? ? 12.71 +2.29 +18 $15.00 118
- 57. 9 x 100X = 1035 100 115 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. 8.59 12 8.59X = 1200 100 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. 8.59 3.41 8.59X = 341 100 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. 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. 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
- 62. Works Cited All images retrieved from Google images
Editor's Notes
- #10: You can only use this when given the whole or starting amount before a change happens
- #12: You can only use this when given the whole or starting amount before a change happens
- #15: You can only use this when given the whole or starting amount before a change happens
- #18: You can only use this when given the whole or starting amount before a change happens
- #21: You can only use this when given the whole or starting amount before a change happens
- #28: You can only use this when given the whole or starting amount before a change happens
- #35: You can only use this when given the whole or starting amount before a change happens
- #42: You can only use this when given the whole or starting amount before a change happens
- #49: You can only use this when given the whole or starting amount before a change happens
- #50: All you need is at least 2 other boxes filled in… This is what each box represents… Addition or Subtraction from what you start with which is 100% then the result is part of the whole even if it is more than what you started with then you will have over 100%