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