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Which of the following is an irreducible fraction?

(a) $\frac{105}{112}$
(b) $\frac{66}{77}$
(c) $\frac{46}{63}$
(d) $\frac{51}{85}$

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Solution

(c) $\frac{46}{63}$

A fraction $\frac{a}{b}$ is said to be irreducible or in its lowest terms if the HCF of a and b is 1.
46 = 2 $\times$ 23 $\times$ 1
63 = 3 $\times$ 3 $\times$ 21 $\times$ 1

Clearly, the HCF of 46 and 63 is 1.

Hence, $\frac{46}{63}$ is an irreducible fraction.

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