QUANTITATIVE LITERACY WORKSHOP
PERCENTAGES
A fraction whose denominator is 100 is called a percent. The meaning of the word percent is
1
37
hundredth (per hundred). (Bobrow 1985:52) Percent is written as %
, so that 37%
.
100
100
LO (LEARNING OUTCOMES):
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.
0.05
Changing decimals to percents
Changing percents to decimals
Changing fractions to percents
Change percents to fractions
Time savers
Finding a percent of a number
Percent - other applications
Percent - proportion method
Finding the percent increase or percent decrease
Percent – word problems
CHANGING DECIMALS TO PERCENTS
100
100
(0.05 100)
1
100
1
100
5%
5
Multiplying and dividing by the same number,
100
1 , enlarges the decimal. Notice how the
100
decimal point moved two places to the right.
The steps to change decimals to percents:
1. Move decimal point two places to the right (it may be necessary to add zeros)
2. Insert a percent sign
Examples
0.17 0.17. 17%
0.0012 0.00.12 0.12%
10.1 10.10. 1010%
Exercise: Change each decimal to a percent
0.77 1.85 0.005 20.3 0.8
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2.
CHANGING PERCENTS TO DECIMALS
75% 75
1
100
75
100
0.75
Notice how the decimal point moved two places to the left and the percent sign disappeared.
The steps to change percents to decimals:
1. Eliminate the percent sign
2. Move decimal point two places to the left (it may be necessary to add zeros)
Examples
5% 0.05. 0.05
20% 0.20. 0.2
31.1% 0.31.1 0.311
Exercise: Change each percent to a decimal
123% 2% 80% 0.4% 0.01%
3.
CHANGING FRACTIONS TO PERCENTS
2.decimal
36
40
9
10
1. fraction
0.9
100
100
percent
1
100
0.9 100
90%
decimal
Steps changing fractions to percents:
Option 1: If the denominator is a factor of 100
1. Enlarge the fraction by multiplying and dividing the numerator and the denominator by
the same number so that the denominator becomes 100.
2. Replace the denominator with a percent sign.
Examples
1
2
1 50
2 50
50
100
3
5
50%
3 20
5 20
60
100
5
4
60%
5 25 125
125%
4 25 100
Option 2: Alternative method
1. Change the fraction to a decimal
2. Change the decimal to a percent (see LO 1 steps)
Examples
3
1
3
3
8
8
0.125
0.375 37.5%
2
3
2
1
3
2
0.33 13
0.66 23
66 23 %
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2
2.5 250%
2
Exercise: Change each fraction to a percent
7
6
3
20
24
4.
33
3
7
49
7
2
CHANGING PERCENTS TO FRACTIONS
75% 75
1
100
75
100
3
4
The steps to change percents to fractions:
1. Drop the percent sign.
2. Write over one hundred.
3. Simplify if necessary
Examples
30%
30
100
3
10
232%
232
100
116
50
2
8
25
13%
13
100
Exercise: Change each percent to a fraction
120% 2% 35% 0.4% 0.012%
5.
TIME SAVERS
Learning the following can eliminate unnecessary computations.
1
100
1
10
2
5
7
10
1
3
3
8
1
6
1
0.01 1%
0.1 10%
4
10
0.4 40%
0.7 70%
0.33 13
33 13 %
0.375 37.5%
0.16 23 16 23 %
1.00 100%
1
4
1
5
1
2
4
5
2
3
5
8
5
6
2
25
0.25 25%
100
2
0.2 20%
10
5
0.5 50%
10
8
0.8 80%
10
0.66 23
66 23 %
0.625 62.5%
0.83 13
83 13 %
3
4
3
10
3
5
9
10
1
8
7
8
1
3
2
75
100
0.75 75%
0.3 30%
6
10
0.6 60%
0.9 90%
0.125 12.5%
0.875 87.5%
3.5 350%
2.00 200%
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6.
FINDING A PERCENT OF A NUMBER
What is 20% of 80?
20% 80
20
1600
80
16 or 20% 80 0.2 80 16.00 16
100
100
The steps to finding a percent of a number:
Note: The word of means multiple
1. Let the number be x
2. Change the percent to a fraction or decimal (whichever one is easier)
3. and multiply
Examples
What is 50% of 12?
x 50% 12
What is
x
50
600
12
100
100
6 or x 50% 12 0.5 12 6
1
% of 36?
2
1
1
2
% 36
36
2
100
1
36
200
36
200
9
50
0.18 or x
1
% 36 0.005 36 0.18
2
Exercise: Finding percent of a number
What is 16% of 25?
7.
What is 70% of 20?
What is
1
% of 1000?
4
PERCENT – OTHER APPLICATIONS
Turn the question word-for-word into an equation. (Bobrow 1985:55)
Step
1. Substitute for the following
a. what x
b. is
(equal sign)
c. of
(the multiplication sign)
2. Change percents to decimals or fractions
3. Solve the equation
Examples
18 is what percent of 90?
10 is 50% of what number?
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50
x
100
100
10
x
50
18 x 90
18
x
90
x
10
1
5
0.2 20%
x 20
What is 15% of 60?
15
60
100
90
x
10
9
x
Exercise: Percent – other applications
18 is what percent of 45?
8.
12 is 24% of what number?
What is 65% of 30?
PERCENT – PROPORTION METHOD
A simple method commonly used to solve percent problems
Examples
30 is what percent of 50?
?
?
1. Set up a blank proportion
?
?
2. Now fill in the empty spaces
a. What is next to the percent (%) is put over 100. The word what is the unknown x )
x
?
100 ?
b. Whatever comes immediately after the word of goes on the bottom of the one side
x
?
of the proportion
100 50
c. What is left (comes next to the word is) goes on the top, on one of the sides of the
x
30
proportion
100 50
d. Solve the proportion
60 30
Therefore 60%
100 50
(Solving mechanically would not be time effective)
This method works for three basic types of percent questions
1. 30 is what percent of 50?
2. 30 is 10% of what number?
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3. What number is 40% of 50? (easier to simply multiply the numbers)
Exercise: Percent – proportion method
40 is what percent of 160?
60 is 30% of what number?
What percent of 25 is 12?
70% of what number is 35?
What number is 15% of 40?
9.
FINDING THE PERCENT INCREASE OR PERCENT DECREASE
To find the percent change (increase or decrease) use the following formula:
change
starting point
percent change
Terms percent rise, percent difference and percent change are the same as percent change.
Examples:
What is the percent decrease of a R250 item on sale to R200?
Change: 250 200 50
change
starting point
50
250
1
5
20% decrease
What is the percent increase of John’s salary if it went from R1500 a month to R2000 a month?
Change: 2000 1500 500
change
starting point
500
1500
1
33.3% increase
3
Exercises: Finding Percent Increase or Percent Decrease Problems.
1. Find the percent decrease from 162 to 108
2. What is the percent difference between a first month’s rent of R2800 and second month’s
rent of R3000?
3. What is the percent increase in rainfall from January (6 mm) to February (10mm)?
4. What is the percent change from 1,200 to 1,890?
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10.
PERCENT – WORD PROBLEMS
Sixty four students are awarded doctoral degrees in the CSET, and this number comprises 40% of the
total PhD graduate student body. How many PhD students were enrolled?
First circle what you have been asked to find – how many graduate students. Now in order to plug
into the percentage equation
is
of
%
try rephrasing the question into a simple sentence.
In this case
64 is 40% of what total?
Note that the 64 sits next the word is; therefore 64 is the ‘is’ number. 40 is the percent. Notice that
what total sits next to the word of. Therefore, plugging into the equation,
is
of
64
x
Cross multiplying
%
40
100
40x 6400
40 x 6400
40
40
x 160
Therefore, the total number of PhD graduates in CSET was 160 students.
Exercise:
In a school of five hundred and fifty learners, sixty six do not sign up for after-school sports. What
percent of the school signs up for after school sport?
ANSWERS TO EXERCISES
1.
Change each decimal to a percent
0.77 77% 1.85 185% 0.005 0.5% 20.3 2030% 0.8 80%
2.
Change each percent to a decimal
123% 1.23 2% 0.02 80% 0.8 0.4% 0.004 0.01% 0.0001
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3.
Change each fraction to a percent
7
20
28% 3
6
1
33
7
3
3.25 325%
11 1100%
24
4
3
49
Change each percent to a fraction
120 1
2
1
35
120%
1
2%
35%
100
5
100 50
100
0.142857143 14.3%
3 75
4 100
4.
0.4
100
0.4%
2
5
100
2
500
1
250
0.012%
7
20
0.012
100
12
1000
3
250
100
100
3
25000
6.
Finding percent of a number
16
16
70
x
25
4%
x
20 14%
100
4
100
x
1
4
100
7.
1000
1
4
10 0.25 10 2.5%
Percent – other applications
x
18
x
8.
x 12
65
30
100
195
x
10
19.5
x
100
24
50
Percent – proportion method
x
40
100 160
160 x 40 100
x
x
9.
12 24% x
x 45
18
45
2
40%
5
65% 30
4000
160
25%
30 60
100 x
30 x 60 100
x
x
x
12
100 25
25 x 12 100
60 100
30
200
70 35
100 x
70 x 35 100
12 100
25
x 48
35 100
70
x 50
x
x
15
100
x
40
15 40
x
100
x 6
Percent – Finding Percent Increase or Percent Decrease
1.
change
starting point
162 108 54
162
162
2.
change
starting point
200
2800
1
14
3.
change
starting point
4
6
66 23 % decrease
2
3
3
9
1
=33.3% decrease
3
7.14% increase
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75%
4.
10.
change
starting point
690
1200
0.575 57.5% increase
Percent – Word Problems
First circle what you have been asked to find – what percent...signs up. Now using the information
given in the problem, plug into the percentage equation. Note that since 66 learners do not sign up
for the after-school sports, the number that does sign up must be the total number of learners
minus 66, i.e. 550-66=484. The problem may be reworded as 484 learners is what percent of 550.
is
of
484
550
Cross multiplying
%
x
100
550x 48400
550 x 48400
550
550
x 88
Therefore 88% of the school signs up for after-school sports.
REFERENCES
Bobrow, J. (1985) Math Review for Standardized Tests. Nebraska: Cliffs Notes Inc. 422p. ISBN 08220-2033-5
Singleton, J. and Bohlman, C. (2009) Mathematics Access Module. Pretoria: University of South
Africa.
KATE STRYDOM
2011
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