# 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?

# We can solve this question by comparing the fractions.

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

Let's compare the given fractions.

**Explanation:**

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

### (4) 3/5 < 11/15 < 2/3

### 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