The fractions `(1)/(3),(4)/(7) and (2)/(5)` written in ascending order given by :

Options

A. `(4)/(7) lt (1)/(3) lt (2)/(5)`
B. `(2)/(5) lt (4)/(7) lt (1)/(3)`
C. `(1)/(3) lt (2)/(5) lt (4)/(7)`
D. `(4)/(7) gt (1)/(3) gt (2)/(5)`

Answer

To arrange the fractions \( \frac{1}{3}, \frac{4}{7}, \) and \( \frac{2}{5} \) in ascending order, we can compare their values. Here’s a step-by-step solution:

### Step 1: Convert each fraction to a decimal
To compare the fractions easily, we can convert each fraction to its decimal form.

1. **For \( \frac{1}{3} \)**:
\[ \frac{1}{3} \approx 0.3333 \]

2. **For \( \frac{4}{7} \)**:
\[ \frac{4}{7} \approx 0.5714 \]

3. **For \( \frac{2}{5} \)**:
\[ \frac{2}{5} = 0.4 \]

### Step 2: Compare the decimal values
Now we can compare the decimal values we calculated:

- \( 0.3333 \) (from \( \frac{1}{3} \))
- \( 0.4 \) (from \( \frac{2}{5} \))
- \( 0.5714 \) (from \( \frac{4}{7} \))

### Step 3: Arrange in ascending order
From the decimal values, we can see that:

1. \( 0.3333 \) (smallest) corresponds to \( \frac{1}{3} \)
2. \( 0.4 \) (next) corresponds to \( \frac{2}{5} \)
3. \( 0.5714 \) (largest) corresponds to \( \frac{4}{7} \)

Thus, the fractions in ascending order are:
\[ \frac{1}{3}, \frac{2}{5}, \frac{4}{7} \]

### Final Answer:
The fractions in ascending order are \( \frac{1}{3}, \frac{2}{5}, \frac{4}{7} \).

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