Question

Mark the correct alternative in each of the following:

The fraction $\frac{84}{98}$ in its lowest terms is

(a) $\frac{42}{49}$ (b) $\frac{12}{14}$ (c) $\frac{6}{7}$ (d) $\frac{3}{7}$

Answer 1

Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Factors of 98: 1, 2, 7, 14, 49, 98

Common factors of 84 and 98: 1, 2, 14

∴ HCF of 84 and 98 = 14

Now,

$\frac{84}{98}=\frac{84÷14}{98÷14}=\frac{6}{7}$ (Dividing numerator and denominator by the HCF of 84 and 98 i.e. 14)

Hence, the correct answer is option (c).