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12
example 2: Find two equivalent fractions of .
18
12 12 ÷ 2 6 12 12 ÷ 3 4 Think and Answer
Solution: We have, = = and = =
18 18 ÷ 2 9 18 18 ÷ 3 6 3 = 12 =
6 4 12 20 45
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: Reducing the following fractions to their simplest form.
108 135
(a) (b)
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.

Now, 108 = 108 ÷ 18 = 6
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 Think and Answer
3 15 3 75
5 5 5 25 Is every unit fraction
1 5 5 in its 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.

135 135 ÷ 15 9
Now, = =
300 300 ÷ 15 20

Thus, 9 is the simplest form of 135 .
20 300

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