Question

Mark the correct alternative in each of the following:

Which of the following fraction is an irreducible (or in its lowest terms)?

(a) $\frac{91}{104}$ (b) $\frac{105}{112}$ (c) $\frac{51}{85}$ (d) $\frac{43}{83}$

Answer 1

We know that a fraction is irreducible (or is in its lowest terms) if the HCF of its numerator and denominator is 1.

Consider the fraction $\frac{91}{104}$.

HCF of 91 and 104 = 13 ≠ 1

So, the fraction $\frac{91}{104}$ is reducible.

Consider the fraction $\frac{105}{112}$.

HCF of 105 and 112 = 7 ≠ 1

So, the fraction $\frac{105}{112}$ is reducible.

Consider the fraction $\frac{51}{85}$.

HCF of 51 and 85 = 17 ≠ 1

So, the fraction $\frac{51}{85}$ is reducible.

Now,

Consider the fraction $\frac{43}{83}$.

HCF of 43 and 83 = 1

So, the fraction $\frac{43}{83}$ is irreducible (or is in its lowest terms).

Hence, the correct answer is option (d).