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12
Example 2: Find two equivalent fractions of .
18 Think Tank Logical Thinking

Solution: We have: 12 = 12 ÷ 2 = 6 I am a proper fraction. The
sum of my numerator and denominator
18 18 ÷ 2 9 is 15. The product of my numerator

and 12 = 12 ÷ 3 = 4 and denominator is 54. What fraction
am I? Now, find two fractions that are
18 18 ÷ 3 6 equivalent to me.
6 4 12
Hence, and are equivalent fractions of .
9 6 18

rEducing a Fraction to its lowEst tErMs

A fraction is said to be in its lowest term (or simplest form), if the numerator and the
denominator of the fraction have no common factor except 1.
To reduce a fraction to its lowest term, the numerator and the denominator of the fraction
are divided by their HCF.

Example: Reduce the following fractions to their simplest form.
( a) 108 (b) 135
126 300
Solution: (a) First, we find the HCF of the numerator 108 and the denominator 126.

2 108 2 126
2 54 3 63
3 27 3 21
3 9 7 7
3 3 1
1

Clearly, 108 = 2 × 2 × 3 × 3 × 3 and 126 = 2 × 3 × 3 × 7.
Therefore, HCF of 108 and 126 = 2 × 3 × 3 = 18.
108 108 ÷ 18 6
N o w , = =
126 126 ÷ 18 7

Thus, 6 is the simplest form of 108 .
7 126
( b) First, we find the HCF of the numerator 135 and the denominator 300.
3 135 2 300
3 45 2 150
3 15 3 75 Think Tank Logical Thinking
5 5 5 25 Is every unit fraction in its
1 5 5 simplest form?
1
Clearly, 135 = 3 × 3 × 3 × 5 and 300 = 2 × 2 × 3 × 5 × 5.
Therefore, HCF of 135 and 300 = 3 × 5 = 15.

N o w , 135 = 135 ÷ 15 = 9
300 300 ÷ 15 20
9 135
Thus, is the simplest form of .
20 300

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