Solve: `(12)/(13) xx (285)/(96) div (171)/(169)` =?
A. `3(2)/(3)`
B. `2(17)/(24)`
C. `(7)/(8)`
D. `(11)/(24)`

Options

A. C
B. D
C. B
D. A

Answer

To solve the expression \((12/13) \times (285/96) \div (171/169)\), we will follow these steps:

### Step 1: Rewrite the expression
We start by rewriting the division as multiplication by the reciprocal:
\[ \frac{12}{13} \times \frac{285}{96} \div \frac{171}{169} = \frac{12}{13} \times \frac{285}{96} \times \frac{169}{171} \]

### Step 2: Multiply the fractions
Now we can multiply the fractions together:
\[ \frac{12 \times 285 \times 169}{13 \times 96 \times 171} \]

### Step 3: Simplify the fractions
Before calculating, we can simplify the fractions by canceling common factors:
- The numerator: \(12\) and \(96\) can be simplified. \(12\) goes into \(96\) \(8\) times.
- The denominator: \(171\) can be factored as \(3 \times 57\) and \(285\) can be factored as \(3 \times 95\), allowing us to cancel \(3\).

After canceling:
\[ \frac{1 \times 285 \times 169}{13 \times 8 \times 57} \]

### Step 4: Calculate the remaining values
Now we compute the values:
- \(285\) divided by \(13\) gives \(21.923\) (approximately, but we will keep it as a fraction for accuracy).
- \(57\) multiplied by \(8\) gives \(456\).

Thus:
\[ \frac{285 \times 169}{13 \times 456} \]

### Step 5: Final calculation
Now we compute \(285 \times 169\) and \(13 \times 456\):
- \(285 \times 169 = 48165\)
- \(13 \times 456 = 5928\)

Now we have:
\[ \frac{48165}{5928} \]

### Step 6: Simplify the final fraction
To simplify \(\frac{48165}{5928}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD). After calculating, we find:
\[ \frac{48165 \div 1923}{5928 \div 1923} = \frac{25}{3} \]

### Step 7: Convert to mixed fraction
Converting \(\frac{25}{3}\) into a mixed fraction gives us:
\[ 8 \frac{1}{3} \]

Thus, the final answer is:
\[ \frac{217}{24} \]

### Conclusion
The answer is \(2 \frac{17}{24}\), which corresponds to option B.