Page 68 - Mathematics

or dividing both terms of a ratio by the a : b = 3: 6
same number does not change the ratio. b : c 6:10=
In other words, 2: 4 4:8 (multiplying 3: 6 :10 and
each term of the ratio by 2). The ratio Therefore, : :abc =
: =
can be reduced to its lowest terms by ac 3:10.
expressing the ratio as a fraction and
simplify it to its lowest term. Example 4.3

Example 4.1 Jaha and Siwema shared 40,000
Tanzanian shillings. Jaha received
Simplify 48:36. 15,000 Tanzanian shillings and Siwema
Tanzania Institute of Education
received 25,000 Tanzanian shillings.
Solution Find the ratio of the amount of money
Given 48:36 each of them received.
The Given ratio can be written in

fraction as 48 Solution
36 The ratio is written as 15,000 to

Dividing the numerator and 25,000 or
denominator by 12 gives, 15,000 25,000÷ = 15,000
48 = 4 25,000

36 3 = 3
Therefore, 48:36 in its simplified 5
form is 4:3. Therefore, the ratio of the amount of
money received by Jaha and Siwema
Example 4.2 is 3:5.

Given a:b = 1:2 and b:c = 3:5, find Example 4.4
a:b:c and a:c.

Solution A man’s monthly income is
Given :ab = 1: 2 and :bc = 3:5. 1,274,000 Tanzanian shillings.
He spends 1,078,000 Tanzanian
Mathematics Form One by 2 as follows: 3:5 ratio between his income to
b is in both ratios, so make the two
shillings every month. Find the
ratios equivalent by multiplying
1: 2 by 3 and :bc =
ab
:
expenditure and savings to income.
Solution
: ab =
(1: 2) 3×
Income to expenditure ratio:
: bc =
(3:5) 2×

62 Given, income = Tshs 1,274,000

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Mathematics form 1.indd 62