If the fractions `2/5, 3/8, 4/9, 5/13 and 6/11` are arranged in ascending order, which one will be fourth place?

Options

A. `3/8`
B. `4/9`
C. `5/13`
D. `6/11`

Answer

To determine which fraction is in the fourth place when the fractions \( \frac{2}{5}, \frac{3}{8}, \frac{4}{9}, \frac{5}{13}, \frac{6}{11} \) are arranged in ascending order, we can follow these steps:

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

1. \( \frac{2}{5} = 0.4 \)
2. \( \frac{3}{8} = 0.375 \)
3. \( \frac{4}{9} \approx 0.444 \) (approximately, since \( \frac{4}{9} = 0.4444... \))
4. \( \frac{5}{13} \approx 0.3846 \) (approximately)
5. \( \frac{6}{11} \approx 0.5454 \) (approximately)

### Step 2: List the decimal values
Now we list the decimal values we calculated:
- \( \frac{3}{8} \approx 0.375 \)
- \( \frac{5}{13} \approx 0.3846 \)
- \( \frac{2}{5} = 0.4 \)
- \( \frac{4}{9} \approx 0.444 \)
- \( \frac{6}{11} \approx 0.5454 \)

### Step 3: Arrange the fractions in ascending order
Now we can arrange the decimal values in ascending order:
1. \( 0.375 \) (which is \( \frac{3}{8} \))
2. \( 0.3846 \) (which is \( \frac{5}{13} \))
3. \( 0.4 \) (which is \( \frac{2}{5} \))
4. \( 0.444 \) (which is \( \frac{4}{9} \))
5. \( 0.5454 \) (which is \( \frac{6}{11} \))

### Step 4: Identify the fourth place
From the arranged list, we can see that the fourth fraction in ascending order is:
- \( \frac{4}{9} \)

### Conclusion
Thus, the fraction that is in the fourth place when arranged in ascending order is \( \frac{4}{9} \).

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