`4 (4)/(5) + (3)/(7) "of 7" + (4)/(5) xx (3)/(10) - (1)/(5)` is equal to :

Options

A. `(7)/(5)`
B. `(8)/(5)`
C. `(34)/(25)`
D. `(196)/(25)`

Answer

To simplify the expression \(4 \frac{4}{5} + \frac{3}{7} \text{ of } 7 + \frac{4}{5} \times \frac{3}{10} - \frac{1}{5}\), we will follow these steps:

### Step 1: Convert mixed numbers to improper fractions
Convert \(4 \frac{4}{5}\) to an improper fraction:
\[ 4 \frac{4}{5} = \frac{4 \times 5 + 4}{5} = \frac{20 + 4}{5} = \frac{24}{5} \]

### Step 2: Simplify the "of" operation
The term \(\frac{3}{7} \text{ of } 7\) can be simplified as:
\[ \frac{3}{7} \times 7 = 3 \]

### Step 3: Calculate the multiplication
Now, calculate \(\frac{4}{5} \times \frac{3}{10}\):
\[ \frac{4}{5} \times \frac{3}{10} = \frac{4 \times 3}{5 \times 10} = \frac{12}{50} \]

### Step 4: Rewrite the expression
Now substitute back into the expression:
\[ \frac{24}{5} + 3 + \frac{12}{50} - \frac{1}{5} \]

### Step 5: Find a common denominator
The least common multiple (LCM) of the denominators (5 and 50) is 50. Convert each term:
- \(\frac{24}{5} = \frac{24 \times 10}{5 \times 10} = \frac{240}{50}\)
- \(3 = \frac{3 \times 50}{50} = \frac{150}{50}\)
- \(\frac{12}{50}\) remains as it is.
- \(-\frac{1}{5} = -\frac{1 \times 10}{5 \times 10} = -\frac{10}{50}\)

### Step 6: Combine the fractions
Now combine all the fractions:
\[ \frac{240}{50} + \frac{150}{50} + \frac{12}{50} - \frac{10}{50} = \frac{240 + 150 + 12 - 10}{50} = \frac{392}{50} \]

### Step 7: Simplify the fraction
Now simplify \(\frac{392}{50}\):
\[ \frac{392 \div 2}{50 \div 2} = \frac{196}{25} \]

### Final Answer
Thus, the simplified expression is:
\[ \frac{196}{25} \]