STRAND: Number
TOPIC:
Percentages
Expressing one number as a percentage
of another (worded questions)
To express one number as a percentage of another number, form a fraction using the two numbers and multiply it by 100.
When forming a fraction, the number that is being expressed as a percentage must be placed in the numerator.
WORKED Example
At a Junior Secondary College, 72 out of 320 students did not play a competition sport during the
summer season. Express the number of students not involved in a competition sport as a percentage of
the total number of students in this college.
Solution
We need to express 72 (the number of students not involved in sport) as a percentage of 320 (the total
number of students). Form a fraction by placing 72 (the number that is being expressed as a percentage) in
the numerator and multiply it by 100.
72
--------320
× 100 =
72
--------320
×
(Express 100 as a fraction by putting it over 1.)
=
7200
------------ %
320
(Multiply the numerators together and the denominators together.)
=
45
------ %
2
(Simplify by dividing the numerator and the denominator by 160: the HCF.)
= 22 1--2- %
Therefore,
sport.
100
--------1
22 1--2- %
(Convert the improper fraction into a mixed number.)
of the 320 students at this Junior Secondary College are not involved in a competition
Try these
1 Ben wrote 20 letters, while Emily wrote 40. Express the number of letters written by Ben as a percentage of the number of
letters written by Emily.
2 The price of a particular chocolate increased from $1.20 in 1980 to $3.60 in the year 2000. Express the price of chocolate
in 1980 as a percentage of the price of the same chocolate in the year 2000.
3 The area of an oval is two-seventh of the area of a school ground. Express the area of the oval as a percentage of the area
of the school ground.
4 The length of a piece of string is 60 cm, while the length of a piece of wire is 80 cm. Express the length of the string as a
percentage of the length of the wire.
5 The volume of a cone is 250 cm3, while the volume of a cylinder with the same radius and height is 750 cm3. Express the
volume of the cone as a percentage of the volume of the cylinder.
6 The area of block A is 77 m2 and the area of block B is 80 m2. Express the area of block A as a percentage of the area of
the block B.
7 Express the height of 75 cm as a percentage of the height of 1 1--4- m.
8 In a diagram, the total area of a shape is 36 cm2, while the area of its shaded part is 24 cm2. Express the shaded area of the
shape as a percentage of its total area.
9 The circumference of a circle is 25π units; the length of arc, subtended by an acute angle in that circle, is 7π units. Express
the length of arc as a percentage of the circumference of a circle.
10 The area of a circle is 48π square units, while the area of a sector cut out from this circle is 12π square units. Express the
area of the sector as a percentage of the area of the circle.
 John Wiley & Sons Australia, Ltd 2001