The arrangement of the fractions $\frac{2}{9}$, $\frac{5}{8}$, $\frac{1}{3}$, $\frac{3}{4}$ in ascending order is

Q: The arrangement of the fractions $\frac{2}{9}$, $\frac{5}{8}$, $\frac{1}{3}$, $\frac{3}{4}$ in ascending order is

To determine the correct arrangement of the fractions $\frac{2}{9}$, $\frac{5}{8}$, $\frac{1}{3}$, and $\frac{3}{4}$ in ascending order, we need to compare their values. The correct answer is given as Option 1: $\frac{2}{9}$, $\frac{1}{3}$, $\frac{5}{8}$, $\frac{3}{4}$. ### Explanation for Option 1: 1. **Convert Fractions to Decimals:** - $\frac{2}{9} \approx 0.222$ - $\frac{1}{3} \approx 0.333$ - $\frac{5}{8} = 0.625$ - $\frac{3}{4} = 0.75$ 2. **Arrange in Ascending Order:** - The smallest decimal is $0.222$ ($\frac{2}{9}$). - The next smallest is $0.333$ ($\frac{1}{3}$). - Followed by $0.625$ ($\frac{5}{8}$). - The largest is $0.75$ ($\frac{3}{4}$). Thus, the fractions in ascending order are $\frac{2}{9}$, $\frac{1}{3}$, $\frac{5}{8}$, $\frac{3}{4}$, which matches Option 1. ### Explanation for Why Other Options are Incorrect: - **Option 2: $\frac{3}{4}$, $\frac{5}{8}$, $\frac{1}{3}$, $\frac{2}{9}$** - This option incorrectly places $\frac{3}{4}$ and $\frac{5}{8}$ before $\frac{1}{3}$ and $\frac{2}{9}$, which is not in ascending order. - **Option 3: $\frac{1}{3}$, $\frac{3}{4}$, $\frac{5}{8}$, $\frac{2}{9}$** - This option incorrectly places $\frac{3}{4}$ before $\frac{5}{8}$ and $\frac{2}{9}$ at the end, which is not in ascending order. - **Option 4: $\frac{2}{9}$, $\frac{1}{3}$, $\frac{3}{4}$, $\frac{5}{8}$** - This option incorrectly places $\frac{3}{4}$ before $\frac{5}{8}$, which is not in ascending order. In conclusion, Option 1 is the correct answer because it accurately arranges the fractions in ascending order based on their decimal equivalents.

Question

Accepted Answer

To determine the correct arrangement of the fractions $\frac{2}{9}$, $\frac{5}{8}$, $\frac{1}{3}$, and $\frac{3}{4}$ in ascending order, we need to compare their values. The correct answer is given as Option 1: $\frac{2}{9}$, $\frac{1}{3}$, $\frac{5}{8}$, $\frac{3}{4}$.

### Explanation for Option 1:

1. **Convert Fractions to Decimals:**
   - $\frac{2}{9} \approx 0.222$
   - $\frac{1}{3} \approx 0.333$
   - $\frac{5}{8} = 0.625$
   - $\frac{3}{4} = 0.75$

2. **Arrange in Ascending Order:**
   - The smallest decimal is $0.222$ ($\frac{2}{9}$).
   - The next smallest is $0.333$ ($\frac{1}{3}$).
   - Followed by $0.625$ ($\frac{5}{8}$).
   - The largest is $0.75$ ($\frac{3}{4}$).

Thus, the fractions in ascending order are $\frac{2}{9}$, $\frac{1}{3}$, $\frac{5}{8}$, $\frac{3}{4}$, which matches Option 1.

### Explanation for Why Other Options are Incorrect:

- **Option 2: $\frac{3}{4}$, $\frac{5}{8}$, $\frac{1}{3}$, $\frac{2}{9}$**
  - This option incorrectly places $\frac{3}{4}$ and $\frac{5}{8}$ before $\frac{1}{3}$ and $\frac{2}{9}$, which is not in ascending order.

- **Option 3: $\frac{1}{3}$, $\frac{3}{4}$, $\frac{5}{8}$, $\frac{2}{9}$**
  - This option incorrectly places $\frac{3}{4}$ before $\frac{5}{8}$ and $\frac{2}{9}$ at the end, which is not in ascending order.

- **Option 4: $\frac{2}{9}$, $\frac{1}{3}$, $\frac{3}{4}$, $\frac{5}{8}$**
  - This option incorrectly places $\frac{3}{4}$ before $\frac{5}{8}$, which is not in ascending order.

In conclusion, Option 1 is the correct answer because it accurately arranges the fractions in ascending order based on their decimal equivalents.