Arrange the fractions in descending order:
`13/(14), 29/(35), 53/(56)`

Answer

To arrange the fractions \( \frac{13}{14}, \frac{29}{35}, \frac{53}{56} \) in descending order, we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM) of the denominators
The denominators are 14, 35, and 56. We need to find the LCM of these numbers.

- The prime factorization of 14 is \( 2 \times 7 \).
- The prime factorization of 35 is \( 5 \times 7 \).
- The prime factorization of 56 is \( 2^3 \times 7 \).

To find the LCM, we take the highest power of each prime:
- For 2: highest power is \( 2^3 \) (from 56).
- For 5: highest power is \( 5^1 \) (from 35).
- For 7: highest power is \( 7^1 \) (common in all).

Thus, the LCM is:
\[ LCM = 2^3 \times 5^1 \times 7^1 = 8 \times 5 \times 7 = 280. \]

### Step 2: Convert each fraction to have the same denominator
Now we will convert each fraction to have a denominator of 280.

1. **For \( \frac{13}{14} \)**:
\[ \frac{13}{14} = \frac{13 \times 20}{14 \times 20} = \frac{260}{280}. \]

2. **For \( \frac{29}{35} \)**:
\[ \frac{29}{35} = \frac{29 \times 8}{35 \times 8} = \frac{232}{280}. \]

3. **For \( \frac{53}{56} \)**:
\[ \frac{53}{56} = \frac{53 \times 5}{56 \times 5} = \frac{265}{280}. \]

### Step 3: Compare the numerators
Now we have the fractions:
- \( \frac{260}{280} \)
- \( \frac{232}{280} \)
- \( \frac{265}{280} \)

We can compare the numerators:
- 260
- 232
- 265

### Step 4: Arrange in descending order
The order from largest to smallest is:
1. \( \frac{265}{280} \) (which is \( \frac{53}{56} \))
2. \( \frac{260}{280} \) (which is \( \frac{13}{14} \))
3. \( \frac{232}{280} \) (which is \( \frac{29}{35} \))

Thus, the fractions in descending order are:
\[ \frac{53}{56}, \frac{13}{14}, \frac{29}{35}. \]