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\ 30-Sep-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

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 the only common factor of 2 and 5 is 1.

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

To write a fraction in its simplest form, divide the numerator and denominator by
the common factors until no common factor (except 1) is left.

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 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