Which of the following is correct:
(1) 2/3 < 3/5 < 11/15
(2) 3/5 < 2/3 < 11/15
(3) 11/15 < 3/5 < 2/3
(4) 3/5 < 11/5 < 2/3

Solution:

To compare the given fractions in each case we will be converting them into Like Fractions

(1) 2/3 < 3/5 < 11/15

The given relationship is incorrect

Let's convert 2/3, 3/5 and 11/15 into like fractions

LCM of 3, 5 and 15 is 15

Thus, the new fractions are 10/15, 9/15 and 11/15

According to the question,

10/15 < 9/15 < 11/15

But 10/15 < 9/15 is incorrect

Hence, the given relationship is incorrect

(2) 3/5 <2/3 <11/15

The given relationship is correct

Let's convert 3/5, 2/3 and 11/15 into like fractions

LCM of 5, 3 and 15 is 15

Thus, the new fractions are 9/15, 10/15 and 11/15

According to the question,

9/15 < 10/15 < 11/15

Hence, the given relationship is correct

(3) 11/15 <3/5 < 2/3

The given relationship is incorrect

Let's convert 11/15, 3/5 and 2/3 into like fractions

LCM of 15, 5 and 3 is 15

Thus, the new fractions are 11/15, 9/15 and 10/15

According to the question,

11/15 < 9/15 < 10/15

But, 11/15 < 9/15 is incorrect

Hence, the given relationship is incorrect

Let's convert 3/5, 11/15 and 2/3 into like fractions

LCM of 5, 15 and 3 is 15

Thus, the new fractions are 9/15, 11/15 and 10/15

According to the question,

9/15 < 11/15 < 10/15

But, 11/15 < 10/15 is incorrect

Hence, the given relationship is incorrect

Thus, option (2) 3/5 <2/3 <11/15 is the correct relationship

Which of the following is correct: (1) 2/3 < 3/5 < 11/15, (2) 3/5 < 2/3 < 11/15, (3) 11/15 < 3/5 < 2/3, (4) 3/5 < 11/5 < 2/3

Summary:

The given option (2) 3/5 < 2/3 < 11/15 is the correct relationship.

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