Remembering Percentage
In math, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred"). It is often denoted using the percent sign, " ". For example (read as "fortyfive percent") is equal to or . Similarly of the total number of students in a class =
Percentage Increase or Decrease
Percentages are often used to express the increase or decrease of a measure relative to its original value. Some real life examples where you come across the changes expressed as percentages are:
Price of gasoline increased from to representing a increase in price
Population of a town declined from to in a decade representing a decline
And finally some of you may weigh twice as much as you were 10 years ago representing a 100% increase in weight!!
Here is a simple three step process to compute percentage changes:
 Identify the change: First step is to find out what is the measure for which the percentage change needs to be calculated. You should identify the final value (i.e. the value after the change has occurred) and the original value (i.e. the value before the increase or decrease). If we are talking about an increase in price from to , our original value is and the final value is .
 Find the change in value: This is the difference between final value and the original value. If we are talking about an increase in price from to , the change in value is
 Express the change as Percentage: This can be easily done by dividing the change in value by the original value and multiplying by : In our example this is equivalent to:
Percentage change =
Percentage change problems are very common on the test. You may find percentage problems in the following situations:
 Two step percentage change problems: In these types of problems you are first expected to calculate the original or final value based on the information provided. The context could be geometry or simple arithmetic. Once you have the original and final value, the question may ask you to calculate percentage changes
 Find the original or final value based on percentage changes: In such problems you are expected to calculate the original value or the final value based on percentage change information.
 Data interpretation: These problems expect you to obtain the final value and the original from graphs and expect you to calculate the percentage changes
Example:
The regular price for a television is $1900. At a sale, George bought the television at a discount of 10%. What was the amount of discount that George got for the television?
A) $19
B) $150
C) $180
D) $190
E) $200
Solution:
Step 1: In this problem we are told that George is getting a discount of 10% and that means there is a percentage decrease of 10%. We are expected to calculate the change in value based on the percentage decrease. Let’s summarize what we know:
To calculate the discount amount, we need to calculate 10% of the regular price i.e. $1900.The discount amount =
The correct answer is D.
Remember, if a quantity is increased or decreased more than once, you cannot simply add or subtract the percentages. You have to work out each increase or decrease step by step.
In order to solve percentage change problems quickly, it’s a good idea to remember some common percentage change values. The following tables show Percentage Increases and Percentage decreases for some commonly used numbers.
Original value 100: Percentage change  Final values
 
Percentage Change

10

20

30

40

50

60

70

80

90

100

150

200

250

400

Increase  Final value

110

120

130

140

150

160

170

180

190

200

250

300

350

500

Decrease  Final value

90

80

70

60

50

40

30

20

10

0

50

100

150

300

Original value 50: Percentage change  Final values
 
Percentage Change

10

20

30

40

50

60

70

80

90

100

150

200

250

400

Increase  Final value

55

60

65

70

75

80

85

90

95

100

125

150

175

250

Decrease  Final value

45

40

35

30

25

20

15

10

5

0

25

50

75

150

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