Simplyfy :
`1 3/4xx2 2/4xx3 4/7`

Options

A. 15
B. 20
C. `7/5`
D. none of these

Answer

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

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \(1 \frac{3}{4}\) to an improper fraction:
\[ 1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \]

2. Convert \(2 \frac{2}{4}\) to an improper fraction:
\[ 2 \frac{2}{4} = \frac{2 \times 4 + 2}{4} = \frac{8 + 2}{4} = \frac{10}{4} = \frac{5}{2} \quad (\text{simplified}) \]

3. Convert \(3 \frac{4}{7}\) to an improper fraction:
\[ 3 \frac{4}{7} = \frac{3 \times 7 + 4}{7} = \frac{21 + 4}{7} = \frac{25}{7} \]

### Step 2: Multiply the Improper Fractions
Now we have:
\[ \frac{7}{4} \times \frac{5}{2} \times \frac{25}{7} \]

### Step 3: Multiply the Numerators and Denominators
1. Multiply the numerators:
\[ 7 \times 5 \times 25 = 875 \]

2. Multiply the denominators:
\[ 4 \times 2 \times 7 = 56 \]

So, we have:
\[ \frac{875}{56} \]

### Step 4: Simplify the Fraction
To simplify \(\frac{875}{56}\), we need to find the greatest common divisor (GCD) of 875 and 56.

1. The prime factorization of 875 is \(5^3 \times 7\).
2. The prime factorization of 56 is \(2^3 \times 7\).

The GCD is \(7\).

Now, divide both the numerator and the denominator by \(7\):
\[ \frac{875 \div 7}{56 \div 7} = \frac{125}{8} \]

### Final Answer
The simplified form of \(1 \frac{3}{4} \times 2 \frac{2}{4} \times 3 \frac{4}{7}\) is:
\[ \frac{125}{8} \]