Arrange the fractions `5/(8), 9/(8), 21/(24), 8/(64)` in descending order.

Answer

To arrange the fractions \( \frac{5}{8}, \frac{9}{8}, \frac{21}{24}, \frac{8}{64} \) in descending order, we will follow these steps:

### Step 1: Identify the fractions
We have the following fractions:
- \( \frac{5}{8} \)
- \( \frac{9}{8} \)
- \( \frac{21}{24} \)
- \( \frac{8}{64} \)

### Step 2: Convert all fractions to have a common denominator
To compare these fractions easily, we can convert them to have a common denominator. The denominators are 8, 8, 24, and 64. The least common multiple (LCM) of these denominators is 64.

Now, we will convert each fraction:

1. **Convert \( \frac{5}{8} \)**:
\[ \frac{5}{8} = \frac{5 \times 8}{8 \times 8} = \frac{40}{64} \]

2. **Convert \( \frac{9}{8} \)**:
\[ \frac{9}{8} = \frac{9 \times 8}{8 \times 8} = \frac{72}{64} \]

3. **Convert \( \frac{21}{24} \)**:
\[ \frac{21}{24} = \frac{21 \times \frac{64}{24}}{24 \times \frac{64}{24}} = \frac{21 \times \frac{8}{3}}{64} = \frac{56}{64} \]
(Here, we multiply both the numerator and denominator by \( \frac{64}{24} \) which simplifies to \( \frac{8}{3} \))

4. **Convert \( \frac{8}{64} \)**:
\[ \frac{8}{64} = \frac{8}{64} \quad (\text{This fraction is already in terms of 64}) \]

### Step 3: List the converted fractions
Now we have:
- \( \frac{40}{64} \)
- \( \frac{72}{64} \)
- \( \frac{56}{64} \)
- \( \frac{8}{64} \)

### Step 4: Arrange the fractions in descending order
Now, we can compare the numerators since they all have the same denominator:
- \( 72 \) (from \( \frac{9}{8} \))
- \( 56 \) (from \( \frac{21}{24} \))
- \( 40 \) (from \( \frac{5}{8} \))
- \( 8 \) (from \( \frac{8}{64} \))

Arranging these from greatest to least gives us:
1. \( \frac{9}{8} \) (or \( \frac{72}{64} \))
2. \( \frac{21}{24} \) (or \( \frac{56}{64} \))
3. \( \frac{5}{8} \) (or \( \frac{40}{64} \))
4. \( \frac{8}{64} \)

### Final Answer
Thus, the fractions in descending order are:
\[ \frac{9}{8} > \frac{21}{24} > \frac{5}{8} > \frac{8}{64} \]