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\\September 11, 2024 12:14 PM Bharat Arora P-6 Reader _________________________ Date: ___________________74

example 2: Is 2 in its simplest form?
5
Solution: Factors of numerator 2 are: 1 and 2.
Factors of denominator 5 are: 1 and 5.

Here, common factor of 2 and 5 is 1.

Thus, 2 is in its simplest form.
5
reducing a Fraction to its simplest Form

To reduce a fraction to its simplest form, we divide the numerator and denominator
of a fraction by the common factors till we get its simplest forms.

example 3: Reduce the following fractions to their simplest forms.
36 56
(a) (b)
45 72
36 36 3 12 3 4 ÷3 ÷3
÷
÷
Solution: (a) = = = 36 12 4
45 45 3 15 3 5 45 = 15 = 5
÷
÷
4 36 ÷3 ÷3
Thus, is the lowest term of .
5 45
÷
÷
÷
56 56 2 28 2 14 2 7 ÷2 ÷2 ÷2
(b) = = = =
÷
÷
÷
72 72 2 36 2 18 2 9 56 = 28 = 14 = 7
72 36 18 9
7 56
Thus, is the lowest term of . ÷2 ÷2 ÷2
9 72
Alternatively
We can also use the method of cancellation to find the simplest form of a given
fraction.

In this method, we find the prime factorisation of the numerator and the denominator,
then cancel the common factors of the numerator and the denominator to get the
simplest form of the given fraction.

example 4: Reduce the following fractions to their simplest forms.

35 17
(a) (b)
63 85
35 5 × 7 5 5 5 35
Solution: (a) = = = Thus, is the simplest form of .
×
××
63 33 7 33 9 9 63
17 17 1 1 17
(b) = = Thus, is the simplest form of .
85 5 × 17 5 5 85

112 Mathematics-4