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.**