Write the following fractions in descending order:
`2/(5), 6/(5), 3/(7), 11/(3), 2(2)/(3)`

Answer

To write the fractions \( \frac{2}{5}, \frac{6}{5}, \frac{3}{7}, \frac{11}{3}, 2 \frac{2}{3} \) in descending order, we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The mixed fraction \( 2 \frac{2}{3} \) can be converted to an improper fraction.

To convert:
- Multiply the whole number (2) by the denominator (3): \( 2 \times 3 = 6 \)
- Add the numerator (2): \( 6 + 2 = 8 \)
- Place this result over the original denominator (3): \( \frac{8}{3} \)

So, \( 2 \frac{2}{3} = \frac{8}{3} \).

### Step 2: List all fractions
Now we have the following fractions:
- \( \frac{2}{5} \)
- \( \frac{6}{5} \)
- \( \frac{3}{7} \)
- \( \frac{11}{3} \)
- \( \frac{8}{3} \)

### Step 3: Find a common denominator
To compare these fractions, we need to find a common denominator. The denominators we have are 5, 7, and 3.

The least common multiple (LCM) of these numbers is 105.

### Step 4: Convert each fraction to have the common denominator
Now we will convert each fraction to have a denominator of 105:

1. **For \( \frac{2}{5} \)**:
\[ \frac{2}{5} = \frac{2 \times 21}{5 \times 21} = \frac{42}{105} \]

2. **For \( \frac{6}{5} \)**:
\[ \frac{6}{5} = \frac{6 \times 21}{5 \times 21} = \frac{126}{105} \]

3. **For \( \frac{3}{7} \)**:
\[ \frac{3}{7} = \frac{3 \times 15}{7 \times 15} = \frac{45}{105} \]

4. **For \( \frac{11}{3} \)**:
\[ \frac{11}{3} = \frac{11 \times 35}{3 \times 35} = \frac{385}{105} \]

5. **For \( \frac{8}{3} \)**:
\[ \frac{8}{3} = \frac{8 \times 35}{3 \times 35} = \frac{280}{105} \]

### Step 5: Compare the numerators
Now we have the following fractions with a common denominator:
- \( \frac{42}{105} \)
- \( \frac{126}{105} \)
- \( \frac{45}{105} \)
- \( \frac{385}{105} \)
- \( \frac{280}{105} \)

Now we can compare the numerators:
- \( 42 \)
- \( 126 \)
- \( 45 \)
- \( 385 \)
- \( 280 \)

### Step 6: Order the fractions in descending order
From the largest to the smallest:
1. \( \frac{385}{105} \) (which is \( \frac{11}{3} \))
2. \( \frac{280}{105} \) (which is \( \frac{8}{3} \))
3. \( \frac{126}{105} \) (which is \( \frac{6}{5} \))
4. \( \frac{45}{105} \) (which is \( \frac{3}{7} \))
5. \( \frac{42}{105} \) (which is \( \frac{2}{5} \))

### Final Answer
Thus, the fractions in descending order are:
\[ \frac{11}{3}, \frac{8}{3}, \frac{6}{5}, \frac{3}{7}, \frac{2}{5} \]