Correct Answer - Option 2 : 11/13
Given,
Four fractions are 9/7, 11/13, 15/17 and 19/21.
Concept used:
The smallest fraction is that whose numerator is smallest if the Denominators of fractions are equal.
Calculation
LCM of 7, 13, 17 and 21 = 4641
To compare these fractions, we have to make Denominator of fractions equal to its LCM.
9/7 = (9 × 663)/(7 × 663)
⇒ 9/7 = 5967/4641
⇒ 11/13 = (11 × 357)/(13 × 357)
⇒ 11/13 = 3927/4641
15/17 = (15 × 273)/(17 × 273)
⇒ 15/17 = 4095/4641
19/21 = (19 × 221)/(21 × 221)
⇒ 19 / 21 = 4199/4641
(3947/4641) has the smallest numerator, which is equivalent to 11/13.
∴ 11/13 is the smallest fraction.
