Page 72 - Mathematics

Proportions Proportions can be written in two ways:
Proportion is essential in solving a c
real-life problems involving scaling, (a) As two equal fractions; = d
b
ratios, and percentages. Such problems (b) Using colons;
involve comparing and relating different When two ratios are equal, that is
quantities. Thus, proportion is a part, a c
: =
a share, or a number considered in ab c :,d it follows that b = d

comparison to a whole. Engage in Thus, a d×= bc× .
Activity 4.2 to recall some real-life
activities on proportions. When three numbers a, b, and c are

in continued proportion, then c is
Tanzania Institute of Education
called the third proportional. The third
Activity 4.2: Relating quantities proportional of two numbers a and b is
a b
:, that is,
1. In your daily life, recall things or defined as :ab = bc b = c .
events for which the occurrence
of one affects the occurrence of Example 4.9
another. Some examples include
number of litres of fuel used by a Find the proportional parts of 156
car per kilometre and number of
people and time used to complete in the ratio 3 : 4 : 5.
a task.
2. Write your own three examples Solution
and show mathematically how Given the total number of parts
the two things or events relate = 156, ratio 3 : 4 : 5.=
to each other. The sum of the terms of the ratio
is 3 + 4 + 5 = 12.
The required proportional parts are:
The concept of equivalent fractions 3
describes correctly what it means by a × 156 39=
1 2 12
proportion. For example, and are
2 4 4 × 156 52=
equivalent, and hence the two fractions 12 × 156 65=
Mathematics Form One are equal. That means, if two ratios are Therefore, the required proportional
are proportional. Thus, a proportion is a
5
statement which shows that two ratios
12
proportional, the corresponding parts of
each ratio have the same relationship.

parts are 39, 52, and 65.

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Mathematics form 1.indd 66