Which among the following is the greatest fraction?

Options

A. `3/7`
B. `3/5`
C. `2/7`
D. `2/5`

Explanation

To determine which among the given fractions is the greatest, we will follow these steps:

### Step 1: List the fractions
The fractions given are:
1. \( \frac{3}{7} \)
2. \( \frac{3}{5} \)
3. \( \frac{2}{7} \)
4. \( \frac{2}{5} \)

### Step 2: Find a common denominator
To compare the fractions, we need to have a common denominator. The denominators here are 7 and 5. We can find the least common multiple (LCM) of these two numbers.

- The LCM of 7 and 5 is 35.

### Step 3: Convert each fraction to have the common denominator
Now we will convert each fraction to have a denominator of 35.

1. For \( \frac{3}{7} \):
\[ \frac{3}{7} = \frac{3 \times 5}{7 \times 5} = \frac{15}{35} \]

2. For \( \frac{3}{5} \):
\[ \frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35} \]

3. For \( \frac{2}{7} \):
\[ \frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35} \]

4. For \( \frac{2}{5} \):
\[ \frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35} \]

### Step 4: Compare the numerators
Now that all fractions have the same denominator, we can compare their numerators:
- \( \frac{15}{35} \)
- \( \frac{21}{35} \)
- \( \frac{10}{35} \)
- \( \frac{14}{35} \)

The numerators are 15, 21, 10, and 14.

### Step 5: Identify the greatest numerator
Among the numerators, the greatest is 21.

### Conclusion
Thus, the greatest fraction is:
\[ \frac{3}{5} \]