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Transcript of Module3
Types of Strategies to Solve Percentage ProblemsBy: Kari Knisely
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
What you will need…
Take notes as needed in order to familiarize yourself with the strategies presented.
Pencil
Paper
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
10% Rule
Move the decimal 1 place to the left
10% of 40
10% of
32.6
10% of 2
10% of
5,345
= 4.0
= 3.26
= .2
= 534.5
10% Rule – Example 1
40% of 25 = ? 10% of 25 = 2.510% of 25 = 2.5
10% of 25 = 2.5
10% of 25 = 2.5
40% of 25
= 10.0
0% 100%50%25% 75%
0 2512.5
6.25
18.75
10
40%
10% Rule –Example 2
30% of 30 = ? 10% of 30 = 3.010% of 30 = 3.010% of 30 = 3.030% of 30
= 9.0
0% 100%50%25% 75%
0 30157.5
22.5
9.0
30%
10% Rule –Example 3
20% of 795 = ?
10% of 795 = 79.510% of 795 = 79.520% of 795
=159.0
0% 100%50%25% 75%
7950 397.5
198.75 596.25
20%
159
Problems when you can apply the 10% Rule
Amount before a change
Can you apply the 10% Rule to these type of problems?
Amount before change
What was the subtotal?
Problems when you can apply the 10% Rule
Amount before a change
Amount after a change
Can you apply the 10% Rule to these type of problems?
Amount after a change
How much total will you leave?
Subtotal$9.00
Amount after a change
How much total will you leave?
Subtotal $9.00
10% of 9.00 = 0.905% of 9.00 = 0.4515% of 9.00 = 1.35Subtotal $ 9.00Tip 1.35Total $10.35
Problems when you can apply the 10% Rule
Amount before a change
Amount after a change
Percent after a change
Can you apply the 10% Rule to these type of problems?
Percent after a change
Subtotal $8.59
Total $12.00(including tip, exclude sales tax)
Percent after a change
Subtotal $8.59Total $12.00(including tip only… ignore sales tax)
10% of $8.59 = .859 = .86
100% Starting Price $8.59
10% of $8.59 = .859 = .86120% $10.3110% of $8.59 = .859 = .86130% $11.1710% of $8.59 = .859 = .86140% $12.03
When you can apply the 10% Rule
Amount before a change
Amount after a change
Percent after a change
Percent of change
Can you apply the 10% Rule to these type of problems?
Percentage of Change
Subtotal $8.59
Total $12.00(including tip and 6% sales tax)
Percentage of Change
Subtotal $8.59Total $12.00(including tip only… ignore sales tax)
Starting Price $8.59+10% of $8.59 = .859 = .86+10% of $8.59 = .859 = .8620% $10.31+10% of $8.59 = .859 = .8630% $11.17+10% of $8.59 = .859 = .8640% $12.03
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
Amount of Change
Subtotal $8.59
Total $12.00(including tip and 6% sales tax)
Must be able to identify parts and whole to use
Need to have 3 of 4 pieces of information
Percent Proportion
Percent Proportion
PartWhole
%100
=isof
%100
=Non Percentage Amount
Non Percentage Amount
Percentage Amount
Percentage Amount
Percent Proportion – Example 1
40% of 25 = ?
0% 100%50%25% 75%
0 2512.5
6.25
18.75
10
40%
isof
%100
=
X25
40100
=
100 X = 25 40100X = 1000
X = 10
Percent Proportion – Example 2
30% of ? is 9
0% 100%50%25% 75%
0 30157.5
22.5
9.0
30%
isof
= %100
9X= 30100
100 9 = X 30900 = 30X
30 = X
Percent Proportion – Example 3
159 is ? % of 795
0% 100%50%25% 75%
7950 397.5
198.75 596.25
20%
159
isof
= %100
159795
= X100
100 159 = 795 X15900 = 795X
20 = X
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
Amount before change
What was the original price?
100 (20-X) = X -202000 – 100X = -
20X2000 = 80X25 = X
Amount after a change
What price will you pay?
$30.00
100 X = 30 25 100X = 750
X = 7.50 $30.00 + 7.50$37.50
Percent after a change
100 -5 = 30 -X-500 = -30X
16.6 = X
100% - 16.6% = 83.3%
Original $30.00
Total $25.00(after discount)
Percent of Change
100 -5 = 30 -X-500 = -30X
16.6 = X
Original $30.00
Total $25.00(after discount)
Amount of Change
Original $30.00
40% discount100 X = 30 -40100X = -1200
X = -12
$12.00
Percent Equation
% Whole = Part
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
Amount before change
How many questions were on the test?
% Whole = Part .80 x = 42
.80x = 42x = 52.5
Approx 53 questions
Amount after a change
How many questions were correct?
% Whole = Part
33.6 = X
.80 42 = X
Approx 34 questions
Percent after a change
What percent of the questions were answered correctly?
% Whole = Part% 42 = 35
% = .83
83%
Percentage of Change
What percent of the questions were answered incorrectly?
% Whole = Part% 42 = 35
% = .83
100% - 83% = 17%
Amount of Change
How many questions were answered incorrectly?
% Whole = Part.83 42 = x
34.86= x42 – 34.86 =
7.14 Approx 7 questions
Percent of Change Equation – Example 1
New – Old
Old
= Percent of Change (as a decimal)
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
Amount before change
What was the original price if purchased in FL?
New – Old Old =
Percent of Change 59.95
- X X
= .06= .06X
59.95
1.06X
59.95 – X =
X=$56.56
Amount after a change
What is the total price after tax?
New – Old Old = Percent
of ChangeX –
59.99 59.99
= .06
3.60X – 59.95
=X
$63.55
=
Percent after a change
Original $79.99Total $62.00(after discount and sales tax)
New – Old Old
=% of Chg
62.00 – 79.99
79.99
=-0.2249
-0.2249 X 100 = -22.5%100% + -22.5% = 77.5%
Percentage of Change
Original $79.99Total $84.49(after sales tax)
*Sale was not in FL
New – Old Old =
% of Chg
84.49 – 79.99
79.99
= .05625
.05625X 100 5.63%
Amount of Change
Original $79.99
*FL Sales Tax is 6%
New – Old Old
= Percent of Change
X – 79.99 79.99
= .06
X – 79.99 = 4.80
X = 84.79
84.79 – 79.99
= $4.80
Tic-Tac-Toe
Whole/Original
Change (+ or -)
Part of Original
100
%
%
Start
+ or -
End
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
Tic-Tac-Toe
Whole/Original
Change (+ or -)
Part of Original
100 %
%
%
Start
+ or -
End
AMOUNT PERCENT
Original starting amount before change
Amount of Change
Percent of Change
Ending amount after change
Ending percent after change
Tic-Tac-Toe
Whole/Original
Change (+ or -)
Part of Original
100 %
%
%
Start
+ or -
End
AMOUNT PERCENT
$40.00-
$8.00
-20
$32.00
80
40100
3280
-8-20
Tic-Tac-Toe
Whole/Original
Change (+ or -)
Part of Original
100 %
%
%
Start
+ or -
End
AMOUNT PERCENT
$40.00-
$8.00
-20
$32.00
80
10040
8032
-20-8
Tic-Tac-Toe
Whole/Original
Change (+ or -)
Part of Original
100 %
%
%
Start
+ or -
End
AMOUNT PERCENT
$40.00-
$8.00
-20
$32.00
80
4032
-832
-2080
10080
40-8
100-20
Tic-Tac-Toe
Whole/Original
Change (+ or -)
Part of Original
100 %
%
%
Start
+ or -
End
AMOUNT PERCENT
$40.00-
$8.00
-20
$32.00
80
3240
32-8
80-20
80100
-840
-20100
Tic-Tac-Toe
Whole/Original
Change (+ or -)
Part of Original
100 %
%
%
Start
+ or -
End
AMOUNT PERCENT
$40.00-
$8.00
-20
$32.00
80
-20-8
-20-8
100X
80XX=40 X=32
Tic-Tac-Toe
Whole/Original
Change (+ or -)
Part of Original
100 %
%
%
Start
+ or -
End
AMOUNT PERCENT
$40.00-
$8.00
-20
$32.00
80
40100
40100
-8X
32X X=80 X=-20
Amount before change
What was the subtotal?
$15.00
+18
118
?
X100
15118
118X = 1500X = 12.71
12.71
+2.29
Amount after a change
How much total will you leave?
Subtotal
$9.00
$9.00
+15
115
?
9100
x115
100X = 1035X = 10.35
$10.35
+1.35
Percent after a change
Subtotal $8.59 Total $12.00
(including tip ONLY)
$8.59
$12.00 ?
8.59100
12X
8.59X = 1200X = 139.70
+3.41
139.70
+39.7
Percentage of Change
Subtotal $8.59 Total $12.00
(including tip ONLY)
$8.59
$12.00
?
8.59100
3.41X
8.59X = 341X = 39.70
+3.41 +39.70
139.7
Amount of Change
Subtotal $8.59 Total $12.00
(including tip ONLY)
$8.59
$12.00
?
12.00 – 8.59= 3.41
+3.41
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
Works Cited
All images retrieved from Google images