Simplify the following :
`2/5" of " 3""4/7-1""1/2 times 7/11`.

Answer

To simplify the expression \( \frac{2}{5} \text{ of } 3 \frac{4}{7} - 1 \frac{1}{2} \times \frac{7}{11} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

1. For \( 3 \frac{4}{7} \):
- Multiply the whole number (3) by the denominator (7): \( 3 \times 7 = 21 \)
- Add the numerator (4): \( 21 + 4 = 25 \)
- Therefore, \( 3 \frac{4}{7} = \frac{25}{7} \).

2. For \( 1 \frac{1}{2} \):
- Multiply the whole number (1) by the denominator (2): \( 1 \times 2 = 2 \)
- Add the numerator (1): \( 2 + 1 = 3 \)
- Therefore, \( 1 \frac{1}{2} = \frac{3}{2} \).

### Step 2: Rewrite the Expression
Now, we can rewrite the expression using the improper fractions:
\[ \frac{2}{5} \times \frac{25}{7} - \frac{3}{2} \times \frac{7}{11} \]

### Step 3: Simplify the First Term
Now we will simplify \( \frac{2}{5} \times \frac{25}{7} \):
- Multiply the numerators: \( 2 \times 25 = 50 \)
- Multiply the denominators: \( 5 \times 7 = 35 \)
- So, \( \frac{2}{5} \times \frac{25}{7} = \frac{50}{35} \).

Now, we can simplify \( \frac{50}{35} \):
- Both 50 and 35 can be divided by 5:
\[ \frac{50 \div 5}{35 \div 5} = \frac{10}{7} \]

### Step 4: Simplify the Second Term
Now we will simplify \( \frac{3}{2} \times \frac{7}{11} \):
- Multiply the numerators: \( 3 \times 7 = 21 \)
- Multiply the denominators: \( 2 \times 11 = 22 \)
- So, \( \frac{3}{2} \times \frac{7}{11} = \frac{21}{22} \).

### Step 5: Subtract the Two Terms
Now we have:
\[ \frac{10}{7} - \frac{21}{22} \]

To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 7 and 22 is 154.

1. Convert \( \frac{10}{7} \) to have a denominator of 154:
- \( \frac{10}{7} = \frac{10 \times 22}{7 \times 22} = \frac{220}{154} \)

2. Convert \( \frac{21}{22} \) to have a denominator of 154:
- \( \frac{21}{22} = \frac{21 \times 7}{22 \times 7} = \frac{147}{154} \)

Now we can subtract:
\[ \frac{220}{154} - \frac{147}{154} = \frac{220 - 147}{154} = \frac{73}{154} \]

### Final Answer
Thus, the simplified expression is:
\[ \frac{73}{154} \]