Correct Answer - Option 4 :
\(\frac{{14}}{{33}}\)
Given:
The numbers are: 8/15, 14/33, 7/13, 11/13
Concept used:
Make the denominators the same and compare the numerators.
The fraction with the least numerator will be the least.
Calculation:
Making the denominators of the fractions same = LCM (15, 33, 13,13) = 13 × 5 × 11 × 3
Let common denominator be D.
Then, 8/15 = (8 × 13 × 11)/(15 × 13 × 11 × 3) = 1,144/D
14/33 = (14 × 5 × 13)/D = 910/D
7/13 = (7 × 5 × 11 × 3)/D = 1,155/D
11/13 = (13 × 5 × 11 × 3)/D = 2,145/D
The numbers are: 1,144/D, 910/D, 1,155/D, 2,145/D
From the above we can see, 910/D is the smallest among all.
∴ We can say that fraction 14/33 is the smallest among all the given fractions.