Simplify:- 3/7 of 49/6 of 4/7=?

Options

A. a. 1
B. b. 2
C. c. 3
D. d. 4

Answer

To simplify the expression \( \frac{3}{7} \times \frac{49}{6} \times \frac{4}{7} \), we can follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \frac{3}{7} \times \frac{49}{6} \times \frac{4}{7} \]

### Step 2: Multiply the fractions
We can multiply the fractions directly:
\[ \frac{3 \times 49 \times 4}{7 \times 6 \times 7} \]

### Step 3: Simplify before multiplying
Now, we can simplify the fractions before multiplying. We can cancel common factors in the numerator and the denominator.

1. **Cancel \(7\) from \(49\)**:
\[ 49 = 7 \times 7 \implies \frac{49}{7} = 7 \]
So, we have:
\[ \frac{3 \times 7 \times 4}{6 \times 7} \]

2. **Cancel \(7\) from the numerator and denominator**:
\[ \frac{3 \times 4}{6} \]

3. **Now, simplify \(3\) and \(6\)**:
\[ \frac{3}{6} = \frac{1}{2} \]
So, we have:
\[ \frac{1 \times 4}{2} = \frac{4}{2} \]

### Step 4: Final simplification
Now, simplify \( \frac{4}{2} \):
\[ \frac{4}{2} = 2 \]

### Conclusion
The simplified result of \( \frac{3}{7} \times \frac{49}{6} \times \frac{4}{7} \) is:
\[ \boxed{2} \]