Page 91 - New Medley 4 Semester 2 PDF (Merged)

Simplest Form of a Fraction

A fraction is said to be in the simplest form or the lowest term, if the
common factor of its numerator and denominator is 1.

3
For example, ; in this fraction, factors of 3 are 1, 3 and factors of 5
5
3
are 1, 5, so their common factor is 1. Thus, is in the lowest term.
5

To reduce a fraction in its simplest form, divide the numerator and the

denominator by their HCF.

Example 3: Are the following fractions in simplest form? If not,

reduce them.
6 11 5 18
(a) (b) (c) (d)
12 20 16 45

6
Solution: (a)
12

Factors of 6 are 1, 2, 3, 6. Factors of 12 are 1, 2, 3,
4, 6, 12.

∴ Common factors are 1, 2, 3, 6.

∴ HCF of 6 and 12 is 6.

Hence, we divide the numerator and the denominator
6
of fraction by 6.
12

6 6÷6 1 1
∴ = = . Thus, is the simplest form.
12 12 ÷6 2 2

11 11
(b) , the HCF of 11 and 20 is 1. Therefore, is in the
20 20

simplest or lowest term.

5
(c) , as 5 and 16 have no common factors other than
16

5
1, so is in the simplest or lowest form.
16
89