Which of the following is correct?

Options

A. `2/3lt3/5lt11/15`
B. `3/5lt2/3lt11/15`
C. `11/15lt3/5lt2/3`
D. `3/5lt11/15lt2/3`

Answer

To determine which of the given options is correct regarding the fractions \( \frac{2}{3} \), \( \frac{3}{5} \), and \( \frac{11}{15} \), we will compare these fractions step by step.

### Step 1: Identify the fractions
The fractions we need to compare are:
- \( \frac{2}{3} \)
- \( \frac{3}{5} \)
- \( \frac{11}{15} \)

### Step 2: Find a common denominator
To compare these fractions easily, we will find the least common multiple (LCM) of the denominators (3, 5, and 15).

- The LCM of 3 and 5 is 15.
- Since 15 is already one of the denominators, we can use 15 as the common denominator.

### Step 3: Convert each fraction to have the common denominator
Now we will convert each fraction to have the denominator of 15:

1. For \( \frac{2}{3} \):
\[ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \]

2. For \( \frac{3}{5} \):
\[ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \]

3. For \( \frac{11}{15} \):
\[ \frac{11}{15} \text{ remains the same.} \]

### Step 4: Compare the fractions
Now we have:
- \( \frac{2}{3} = \frac{10}{15} \)
- \( \frac{3}{5} = \frac{9}{15} \)
- \( \frac{11}{15} \)

We can now compare:
- \( \frac{9}{15} < \frac{10}{15} < \frac{11}{15} \)

This means:
- \( \frac{3}{5} < \frac{2}{3} < \frac{11}{15} \)

### Step 5: Determine the correct option
From our comparison, we can conclude:
- \( \frac{3}{5} < \frac{2}{3} < \frac{11}{15} \)

Thus, the correct option is:
**Option 2: \( \frac{3}{5} < \frac{2}{3} < \frac{11}{15} \)**

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