Arrange the fractions in descending order:
`7/(12), 11/(15), 35/(42)`

Answer

To arrange the fractions \( \frac{7}{12}, \frac{11}{15}, \frac{35}{42} \) in descending order, we need to follow these steps:

### Step 1: Find the LCM of the denominators
The denominators are 12, 15, and 42. We need to find the least common multiple (LCM) of these numbers.

- The prime factorization of 12 is \( 2^2 \times 3^1 \).
- The prime factorization of 15 is \( 3^1 \times 5^1 \).
- The prime factorization of 42 is \( 2^1 \times 3^1 \times 7^1 \).

To find the LCM, we take the highest power of each prime factor:
- For 2: \( 2^2 \) (from 12)
- For 3: \( 3^1 \) (common in all)
- For 5: \( 5^1 \) (from 15)
- For 7: \( 7^1 \) (from 42)

Thus, the LCM is:
\[ LCM = 2^2 \times 3^1 \times 5^1 \times 7^1 = 4 \times 3 \times 5 \times 7 = 420 \]

### Step 2: Convert each fraction to have the same denominator
Now we will convert each fraction to have the denominator of 420.

1. For \( \frac{7}{12} \):
\[ \frac{7}{12} = \frac{7 \times 35}{12 \times 35} = \frac{245}{420} \]

2. For \( \frac{11}{15} \):
\[ \frac{11}{15} = \frac{11 \times 28}{15 \times 28} = \frac{308}{420} \]

3. For \( \frac{35}{42} \):
\[ \frac{35}{42} = \frac{35 \times 10}{42 \times 10} = \frac{350}{420} \]

### Step 3: Compare the numerators
Now we have the fractions:
- \( \frac{245}{420} \)
- \( \frac{308}{420} \)
- \( \frac{350}{420} \)

We can compare the numerators:
- 350 (from \( \frac{35}{42} \))
- 308 (from \( \frac{11}{15} \))
- 245 (from \( \frac{7}{12} \))

### Step 4: Arrange in descending order
The order from greatest to least is:
\[ \frac{35}{42} > \frac{11}{15} > \frac{7}{12} \]

### Final Answer
Thus, the fractions arranged in descending order are:
\[ \frac{35}{42}, \frac{11}{15}, \frac{7}{12} \]

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