Arrange `3/5,7/9,11/13` in descending order.

Options

A. `3/7,7/9,11/13`
B. `7/9,3/5,11/13`
C. `11/13,7/9,3/5`
D. `11/13,3/5,7/9`

Answer

To arrange the fractions \( \frac{3}{5}, \frac{7}{9}, \frac{11}{13} \) in descending order, we will compare their values. We can do this by converting them to a common denominator or by comparing their decimal equivalents. Here, we will use the decimal method for simplicity.

### Step 1: Convert each fraction to a decimal
- For \( \frac{3}{5} \):
\[ \frac{3}{5} = 0.6 \]

- For \( \frac{7}{9} \):
\[ \frac{7}{9} \approx 0.7777\ldots \quad (\text{This is a repeating decimal}) \]

- For \( \frac{11}{13} \):
\[ \frac{11}{13} \approx 0.8461\ldots \]

### Step 2: Compare the decimal values
Now we compare the decimal values obtained:
- \( 0.6 \) (for \( \frac{3}{5} \))
- \( 0.7777\ldots \) (for \( \frac{7}{9} \))
- \( 0.8461\ldots \) (for \( \frac{11}{13} \))

### Step 3: Arrange in descending order
From the decimal values, we can see that:
- \( 0.8461\ldots \) (which is \( \frac{11}{13} \)) is the largest.
- \( 0.7777\ldots \) (which is \( \frac{7}{9} \)) is the second largest.
- \( 0.6 \) (which is \( \frac{3}{5} \)) is the smallest.

Thus, the fractions in descending order are:
\[ \frac{11}{13}, \frac{7}{9}, \frac{3}{5} \]

### Final Answer
The fractions arranged in descending order are:
\[ \frac{11}{13}, \frac{7}{9}, \frac{3}{5} \]

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