3A USES AND ABUSES OF PERCENTAGES
Part 1: Three ways of using percentages
i) Using percentages as fractions
Example
64 % of 1069 people =64 % × 1069 people =684 people
Example You have $ 8 and your friend has $ 4. Then your friend's money is 50 % of yours. Your money is
200 % of your friend's.
ii) Using percentages to describe changes
Example: The population increases from 100000 to 150000. There are two ways to describe the change:
1. Absolute change = 150000-100000=50000
50000
2. Relative change = 100000
× 100% = 50%
Denition The absolute change describes the actual increase or decrease from a reference value/ old value
to a new value.
Absolute change = new value - reference value
The relative change descrives the size of the change compared to the reference value.
absolute change
Relavite change =
.
reference value
Example You now have 2 TV and you used to have 1 more. What is the absolute and relative changes of
the number of TV?
iii) Using percentages for comparisons
Example: John scores 60 pts in a game and Mary scores 50 pts. Two ways to compare Mary's score to John's
score.
(Absolute) Mary scores 10 pts more than John.
(Relative) Mary scores 20% more than John.
Denition
Compare A to B (A is the compared value and B is the reference value)
1
2
3A USES AND ABSUSES OF PERCENTAGES
absolute dierence = compared value -reference value .
Relative dierence =
absolute dierence
× 100%.
reference value
Example Compare Mary's score to John's.
Caution: Be aware of the change of the reference value. e.g. A is 20 % more than B. Then B is not 20 %
less than A. (See the above examples)
3A USES AND ABSUSES OF PERCENTAGES
3
Part 2: Of versus more than
Example Consider the population in City A (200 people) and the population in City B (600 people).
1. Using of: The popolution in A is 33.3 % of that in B. The populaton in B is 600 % of that in A.
2. Using more than: A has 66.7 % more population than B. B has 200 % less popluation than B.
We have the following formulae:
If the compared value is P % more than the reference value, it is (100 + P )% of the reference value. If the
compared value is P % less than the reference value, it is (100 − P )% of the reference value.
Part 3: Solving percentage problems
Basic strategy is to identify the compared value and reference value in the question.
Example If the retail price is 25 % more than the wholesale price and the wholesale price is $ 10, what is
the retail price.
Example A shirt is 25 % o. If you nally pay $ 12.5 (neglecting tax), what is the labelled price?