The fractions $\frac{44}{49}, \frac{33}{38}, \frac{22}{25} ext{ and } \frac{24}{29}$ are written in descending order as

Q: The fractions $\frac{44}{49}, \frac{33}{38}, \frac{22}{25} \text{ and } \frac{24}{29}$ are written in descending order as

The fractions $\frac{44}{49}, \frac{33}{38}, \frac{22}{25} \text{ and } \frac{24}{29}$ are written in descending order as

Question

The fractions $\frac{44}{49}, \frac{33}{38}, \frac{22}{25} 	ext{ and } \frac{24}{29}$ are written in descending order as

Accepted Answer

To determine the correct descending order of the fractions $\frac{44}{49}, \frac{33}{38}, \frac{22}{25}, \text{ and } \frac{24}{29}$, we need to compare their values. The correct order is given as Option 3: $\frac{44}{49}, \frac{22}{25}, \frac{33}{38}, \frac{24}{29}$. Let's justify why this is the correct order.

### Explanation for Option 3:

1. **Comparing $\frac{44}{49}$ and $\frac{22}{25}$:**
   - Convert both fractions to decimals:
     - $\frac{44}{49} \approx 0.897959$
     - $\frac{22}{25} = 0.88$
   - Since $0.897959 > 0.88$, $\frac{44}{49}$ is greater than $\frac{22}{25}$.

2. **Comparing $\frac{22}{25}$ and $\frac{33}{38}$:**
   - Convert both fractions to decimals:
     - $\frac{22}{25} = 0.88$
     - $\frac{33}{38} \approx 0.868421$
   - Since $0.88 > 0.868421$, $\frac{22}{25}$ is greater than $\frac{33}{38}$.

3. **Comparing $\frac{33}{38}$ and $\frac{24}{29}$:**
   - Convert both fractions to decimals:
     - $\frac{33}{38} \approx 0.868421$
     - $\frac{24}{29} \approx 0.827586$
   - Since $0.868421 > 0.827586$, $\frac{33}{38}$ is greater than $\frac{24}{29}$.

Thus, the descending order is $\frac{44}{49}, \frac{22}{25}, \frac{33}{38}, \frac{24}{29}$, which matches Option 3.

### Explanation for Why Other Options are Incorrect:

1. **Option 1: $\frac{24}{29}, \frac{33}{38}, \frac{22}{25}, \frac{44}{49}$**
   - This order incorrectly places $\frac{24}{29}$ as the largest fraction, which is not true as shown by the decimal comparisons.

2. **Option 2: $\frac{22}{25}, \frac{24}{29}, \frac{33}{38}, \frac{44}{49}$**
   - This order incorrectly places $\frac{22}{25}$ before $\frac{44}{49}$, which contradicts the decimal comparison showing $\frac{44}{49}$ is larger.

3. **Option 4: $\frac{44}{49}, \frac{33}{38}, \frac{24}{29}, \frac{22}{25}$**
   - This order incorrectly places $\frac{24}{29}$ before $\frac{22}{25}$, which is incorrect as $\frac{22}{25}$ is larger than $\frac{24}{29}$.

In conclusion, Option 3 is the correct answer as it accurately reflects the descending order of the fractions based on their values.