If the fractions $\frac{2}{5}, \frac{3}{8}, \frac{4}{9}, \frac{5}{13}$ and $\frac{6}{11}$ are arranged in ascending order, which one will be fourth place ?

Q: If the fractions $\frac{2}{5}, \frac{3}{8}, \frac{4}{9}, \frac{5}{13}$ and $\frac{6}{11}$ are arranged in ascending order, which one will be fourth place ?

To determine the correct order of the given fractions $\frac{2}{5}$, $\frac{3}{8}$, $\frac{4}{9}$, $\frac{5}{13}$, and $\frac{6}{11}$ in ascending order, we need to compare their values. One effective way to compare fractions is to convert them to decimal form or find a common denominator. Here, we'll convert them to decimal form for simplicity: 1. $\frac{2}{5} = 0.4$ 2. $\frac{3}{8} = 0.375$ 3. $\frac{4}{9} \approx 0.444$ 4. $\frac{5}{13} \approx 0.385$ 5. $\frac{6}{11} \approx 0.545$ Now, let's arrange these decimal values in ascending order: - $0.375$ ($\frac{3}{8}$) - $0.385$ ($\frac{5}{13}$) - $0.4$ ($\frac{2}{5}$) - $0.444$ ($\frac{4}{9}$) - $0.545$ ($\frac{6}{11}$) From this arrangement, we can see that the fraction $\frac{4}{9}$ is in the fourth position. **Explanation for Option 2 being correct:** - The fraction $\frac{4}{9}$ corresponds to the decimal $0.444$, which is the fourth smallest value when the fractions are arranged in ascending order. Therefore, $\frac{4}{9}$ is correctly placed in the fourth position. **Explanation for why other options are incorrect:** 1. **Option 1 ($\frac{3}{8}$):** This fraction equals $0.375$, which is the smallest value among the given fractions, placing it in the first position, not the fourth. 2. **Option 3 ($\frac{5}{13}$):** This fraction equals approximately $0.385$, which is the second smallest value, placing it in the second position, not the fourth. 3. **Option 4 ($\frac{6}{11}$):** This fraction equals approximately $0.545$, which is the largest value among the given fractions, placing it in the fifth position, not the fourth. Thus, the correct answer is indeed Option 2, $\frac{4}{9}$, as it is the fraction that occupies the fourth position when arranged in ascending order.

Question

Accepted Answer

To determine the correct order of the given fractions $\frac{2}{5}$, $\frac{3}{8}$, $\frac{4}{9}$, $\frac{5}{13}$, and $\frac{6}{11}$ in ascending order, we need to compare their values. One effective way to compare fractions is to convert them to decimal form or find a common denominator. Here, we'll convert them to decimal form for simplicity:

1. $\frac{2}{5} = 0.4$
2. $\frac{3}{8} = 0.375$
3. $\frac{4}{9} \approx 0.444$
4. $\frac{5}{13} \approx 0.385$
5. $\frac{6}{11} \approx 0.545$

Now, let's arrange these decimal values in ascending order:

- $0.375$ ($\frac{3}{8}$)
- $0.385$ ($\frac{5}{13}$)
- $0.4$ ($\frac{2}{5}$)
- $0.444$ ($\frac{4}{9}$)
- $0.545$ ($\frac{6}{11}$)

From this arrangement, we can see that the fraction $\frac{4}{9}$ is in the fourth position.

**Explanation for Option 2 being correct:**
- The fraction $\frac{4}{9}$ corresponds to the decimal $0.444$, which is the fourth smallest value when the fractions are arranged in ascending order. Therefore, $\frac{4}{9}$ is correctly placed in the fourth position.

**Explanation for why other options are incorrect:**
1. **Option 1 ($\frac{3}{8}$):** This fraction equals $0.375$, which is the smallest value among the given fractions, placing it in the first position, not the fourth.
2. **Option 3 ($\frac{5}{13}$):** This fraction equals approximately $0.385$, which is the second smallest value, placing it in the second position, not the fourth.
3. **Option 4 ($\frac{6}{11}$):** This fraction equals approximately $0.545$, which is the largest value among the given fractions, placing it in the fifth position, not the fourth.

Thus, the correct answer is indeed Option 2, $\frac{4}{9}$, as it is the fraction that occupies the fourth position when arranged in ascending order.