Name of Lecturer: Mr. J.Agius
Course: HVAC1
Lesson 16
Chapter 4: Percentages & their Applications

Meaning of a Percentage
“Per cent” means per hundred, i.e. if 60 per cent of the workers in a factory are women it means
that 60 out of every 100 workers are women. If there are 700 workers in the factory, 60  7 =
420 are women, while if there are 1200 workers,
60  12 = 720 are women.
In mathematics we are always looking for shorter ways of writing statements and especially for
symbols to stand for words. The symbol that means “per cent” is % i.e. 60 per cent and 60%
have exactly the same meaning.
60
3
60 per cent means 60 per hundred and this can be written as the fraction
(or by reducing
100
5
terms).
60
3
i.e. 60% of a quantity is exactly the same as
(or ) of that quantity.
100
5
60
If there are 800 cars in a car park and 60% of them are British, then
of the cars are British,
100
60
i.e. the number of British cars is
 800  480
100
Question 1:
What fraction is shaded? Write the fraction in its simplest form.
Write this fraction as a decimal.
Answer:
Fraction =
and Decimal = 0.5.
This is also equal to 50%.
4 Percentages and their Applications
Page 1
Name of Lecturer: Mr. J.Agius

Course: HVAC1
Expressing Percentages as Fractions and Decimals
Example 1
Express
a) 40%
b) 22½ % as fractions in their lowest terms.
Answer
a) 40% =
1
2
40 10
4 2
2


100 10 10 2 5
b) 22 % 
45
45 1
45 5
9
9
%




2
2 100 2  100 5 2  20 40
Example 2
Express
a) 54%
b) 61/2%
c) 271/3 %
as decimals.
Answer
54
 0.54
100
a)
54% 
b)
1
6.5
6 %  6.5% 
 0.065
2
100
c)
1
27.33
27 %  27.33% 
 0.273
3
100
correct to 3 s.f.
Note. Do not forget how we divide by 100.
4 Percentages and their Applications
Page 2
Name of Lecturer: Mr. J.Agius

Course: HVAC1
Changing Fractions and Decimals to Percentages
If 4
of the pupils in a school have been away for a holiday, it means that 80 in every 100 have
5
been on holiday, i.e. 4 is the same as 80%
5
A fraction may be converted into a percentage by multiplying that fraction by 100%. This does
not alter its value, since 100% is 1.
Example 3
Express
7
as a percentage.
20
7
7 20
7

 100 %   5  35%
20 20
1
Answer
 20
To express a decimal as a percentage, we use the same method as we did, when we expressed a
fraction as a percentage.
Example 4

Express
a) 0.7
a)
b)
= 0.7  100% = 70%
= 1.24  100% = 124%
0.7
1.24
b) 1.24
as a percentage.
Comparing Fractions, Decimals and Percentages
Sometimes you will be asked to arrange percentages, fractions and decimals in order of size.
Example 5
Write in order of size, smallest first: 63%,
3
7
, 0.65,
.
5
10
Answer
Write each as a percentage for easy comparison.
Percentage:
63%
3
5
0.65
63%
60%
65%
7
10
70%
Then rearrange them in order of size.
The new order is
4 Percentages and their Applications
3
7
, 63%, 0.65,
5
10
Page 3
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Changing Percentages
Q1
a)
Write these percentages as:
45%
e)
g) 82%
h)
a)
d)
Q3
69%
f)
6%
i)
44%
l)
2
55 %
3
b) 0.9
c)
37
25
9
20
f)
0.83
i)
21
40
l)
0.375
Write these numbers as percentages:
3
4
2
5
e)
g) 0.49
j)
c) 85%
1
12 %
2
1
k) 62 %
4
1
67 %
2
Q2
decimals
fractions in their lowest term.
b) 60%
d) 56%
j)
(a)
(b)
h) 0.36
0.075
k)
7
8
Look at this pie chart.
Other
UK
It shows the amount of sales a company makes in different
parts of the world.
a)
Which of these is the correct answer?
(i)
The amount of sales in the UK is
A
less than 25%
(ii)
The amount of sales in the Rest of Europe is
A
less than 50%
(iii)
The amount of sales in the USA is
A
less than 25%
4 Percentages and their Applications
B
B
B
25%
50%
25%
USA
Rest of
Europe
C
more than 25%
C
more than 50%
C
more than 25%
Page 4
Name of Lecturer: Mr. J.Agius
Q4
Write these in order of size, smallest first:
9
, 0.44
20
11
, 0.64
d) 65%,
16
a)
Q5
49%,
b) 60%, 0.64,
e)
66%,
5
8
c) 0.41,
2
, 38%
5
2
, 0.6
3
Each of these floor designs is made of 100 tiles.
KNIGHT
a)
b)
c)
Q6
Course: HVAC1
DIAMOND
PATHWAYS
What percentage of each design is coloured?
Write each percentage as a fraction in its simplest form.
Write each percentage as a decimal.
Make three floor designs of your own where 20% of the tiles are white and the rest are black.
4 Percentages and their Applications
Page 5