Which of the following is correct?

Options

A. a) `2//3 lt 3//5 lt 11//15`
B. b) `3//5 lt 2//3 lt 11//15`
C. c) `11//15 lt 3//5 lt 2//3`
D. d) `3//5 lt 11//15 lt 2//3`

Answer

To solve the problem, we need to compare the fractions given in the options. Let's go through the steps systematically.

### Step 1: Identify the fractions in each option.
We have three fractions to compare:
1. \( \frac{2}{3} \)
2. \( \frac{3}{5} \)
3. \( \frac{11}{15} \)

### Step 2: Compare the fractions using cross multiplication.
We will compare the fractions pairwise to determine their order.

#### Comparing \( \frac{2}{3} \) and \( \frac{3}{5} \):
- Cross multiply:
- \( 2 \times 5 = 10 \)
- \( 3 \times 3 = 9 \)
- Since \( 10 > 9 \), we have \( \frac{2}{3} > \frac{3}{5} \).

#### Comparing \( \frac{3}{5} \) and \( \frac{11}{15} \):
- Cross multiply:
- \( 3 \times 15 = 45 \)
- \( 5 \times 11 = 55 \)
- Since \( 45 < 55 \), we have \( \frac{3}{5} < \frac{11}{15} \).

#### Comparing \( \frac{2}{3} \) and \( \frac{11}{15} \):
- Cross multiply:
- \( 2 \times 15 = 30 \)
- \( 3 \times 11 = 33 \)
- Since \( 30 < 33 \), we have \( \frac{2}{3} < \frac{11}{15} \).

### Step 3: Summarize the results.
From the comparisons, we can summarize the order of the fractions:
- \( \frac{11}{15} > \frac{2}{3} > \frac{3}{5} \)

### Step 4: Determine the correct option.
Based on the order we found:
- The correct order is \( \frac{11}{15} > \frac{2}{3} > \frac{3}{5} \).
- Therefore, the correct option is **B**: \( \frac{3}{5} < \frac{2}{3} < \frac{11}{15} \).

### Final Answer:
The correct option is **B**.

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