`5(17)/(37)xx4(51)/(52)xx11(1)/(7)+2(3)/(4)=?`

Options

A. 303.75
B. 305.75
C. 303`(3)/(4)`
D. `305(1)/(4)`

Explanation

To solve the expression \( \frac{5(17)}{37} \times \frac{4(51)}{52} \times \frac{11(1)}{7} + \frac{2(3)}{4} \), we will follow these steps:

### Step 1: Simplify each fraction
First, we simplify each fraction in the expression.

1. **First Fraction:**
\[ \frac{5(17)}{37} = \frac{85}{37} \]

2. **Second Fraction:**
\[ \frac{4(51)}{52} = \frac{204}{52} = \frac{51}{13} \quad (\text{after dividing both numerator and denominator by 4}) \]

3. **Third Fraction:**
\[ \frac{11(1)}{7} = \frac{11}{7} \]

4. **Fourth Fraction:**
\[ \frac{2(3)}{4} = \frac{6}{4} = \frac{3}{2} \quad (\text{after dividing both numerator and denominator by 2}) \]

### Step 2: Rewrite the expression
Now we can rewrite the expression with the simplified fractions:
\[ \frac{85}{37} \times \frac{51}{13} \times \frac{11}{7} + \frac{3}{2} \]

### Step 3: Multiply the fractions
Now we will multiply the fractions together:
\[ \frac{85 \times 51 \times 11}{37 \times 13 \times 7} \]

Calculating the numerator:
\[ 85 \times 51 = 4335 \]
\[ 4335 \times 11 = 47685 \]

Calculating the denominator:
\[ 37 \times 13 = 481 \]
\[ 481 \times 7 = 3367 \]

So we have:
\[ \frac{47685}{3367} \]

### Step 4: Add the second fraction
Now we need to add \( \frac{3}{2} \) to this fraction. To do this, we need a common denominator.

The least common multiple (LCM) of 3367 and 2 is:
\[ \text{LCM}(3367, 2) = 6734 \]

Now we convert both fractions to have this common denominator:
1. Convert \( \frac{47685}{3367} \):
\[ \frac{47685 \times 2}{3367 \times 2} = \frac{95370}{6734} \]

2. Convert \( \frac{3}{2} \):
\[ \frac{3 \times 3367}{2 \times 3367} = \frac{10101}{6734} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ \frac{95370 + 10101}{6734} = \frac{105471}{6734} \]

### Step 6: Simplify the final fraction
We can simplify \( \frac{105471}{6734} \) if possible. After checking for common factors, we find that it cannot be simplified further.

### Final Answer
Thus, the final answer is:
\[ \frac{105471}{6734} \]