Which of the following is correct?

a. $ 2 / 3<3 / 5<11 / 15 $

b. $ 3 / 5<2 / 3<11 / 15 $

c. $ 11 / 15<3 / 5<2 / 3 $

d. $ 3 / 5<11 / 15<2 / 3 $

Given:

The fractions in the given options are $\frac{2}{3}$, $\frac{3}{5}$ and $\frac{11}{15}$.

To do:

We have to find which of the given options is correct.

Solution:

To arrange the given options in increasing order, we have to find the LCM of the denominators and convert the fractions to like fractions.

LCM of 3,5 and 15 is 15.            (3 and 5 are factors of 15)
Therefore,

$\frac{2}{3}=\frac{2\times5}{3\times5}=\frac{10}{15}$

$\frac{3}{5}=\frac{3\times3}{5\times3}=\frac{9}{15}$

$\frac{11}{15}$

On comparing the numerators,

9<10<11.

This implies,

$\frac{9}{15}<\frac{10}{15}<\frac{11}{15}$.

Therefore,

$\frac{3}{5}<\frac{2}{3}<\frac{11}{15}$.

Option B is the correct answer. 

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Updated on: 10-Oct-2022

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