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Which of the following is the smallest fraction?

\(\frac{8}{{15}}\)\(\frac{{14}}{{33}}\)\(\frac{7}{{13}}\)\(\frac{{11}}{{13}}\)


1. \(​​\frac{{11}}{{13}}\)
2. \(\frac{8}{{15}}\)
3. \(\frac{7}{{13}}\)
4. \(\frac{{14}}{{33}}\)

1 Answer

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Best answer
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.

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