Arrange the following ratios in descending order. (5:6), (7:8). (9:10)

Answer

To arrange the ratios (5:6), (7:8), and (9:10) in descending order, we will first convert each ratio into a decimal form. This will allow us to compare their values easily.

### Step-by-Step Solution:

1. **Convert the first ratio (5:6) to decimal:**
\[ \text{Decimal value} = \frac{5}{6} \approx 0.8333 \]

2. **Convert the second ratio (7:8) to decimal:**
\[ \text{Decimal value} = \frac{7}{8} = 0.875 \]

3. **Convert the third ratio (9:10) to decimal:**
\[ \text{Decimal value} = \frac{9}{10} = 0.9 \]

4. **Compare the decimal values:**
- \(0.8333\) (for 5:6)
- \(0.875\) (for 7:8)
- \(0.9\) (for 9:10)

5. **Arrange the ratios in descending order based on their decimal values:**
- The largest value is \(0.9\) (9:10)
- The second largest value is \(0.875\) (7:8)
- The smallest value is \(0.8333\) (5:6)

### Final Answer:
The ratios in descending order are:
\[ 9:10, \quad 7:8, \quad 5:6 \]