`(57)/(67)xx(32)/(171)xx(45)/(128)=?`

Options

A. `(15)/(262)`
B. `(15)/(268)`
C. `(15)/(266)`
D. `(17)/(268)`

Explanation

To solve the expression \((57/67) \times (32/171) \times (45/128)\), we can simplify it step by step.

### Step 1: Write the expression
We start with the given expression:
\[ \frac{57}{67} \times \frac{32}{171} \times \frac{45}{128} \]

### Step 2: Combine the fractions
We can combine the fractions into a single fraction:
\[ \frac{57 \times 32 \times 45}{67 \times 171 \times 128} \]

### Step 3: Calculate the numerator
Now we calculate the numerator:
\[ 57 \times 32 \times 45 \]

Calculating step by step:
- First, calculate \(57 \times 32\):
\[ 57 \times 32 = 1824 \]
- Next, multiply the result by 45:
\[ 1824 \times 45 = 82080 \]

So, the numerator is \(82080\).

### Step 4: Calculate the denominator
Now we calculate the denominator:
\[ 67 \times 171 \times 128 \]

Calculating step by step:
- First, calculate \(67 \times 171\):
\[ 67 \times 171 = 11457 \]
- Next, multiply the result by 128:
\[ 11457 \times 128 = 1464576 \]

So, the denominator is \(1464576\).

### Step 5: Write the combined fraction
Now we can write the combined fraction:
\[ \frac{82080}{1464576} \]

### Step 6: Simplify the fraction
To simplify \(\frac{82080}{1464576}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD).

Using a calculator or a GCD method, we find that the GCD of \(82080\) and \(1464576\) is \(1440\).

Now we divide both by \(1440\):
- Numerator:
\[ \frac{82080}{1440} = 57 \]
- Denominator:
\[ \frac{1464576}{1440} = 1016 \]

So, we have:
\[ \frac{57}{1016} \]

### Step 7: Final simplification
We can further simplify \(\frac{57}{1016}\) by dividing both by \(57\):
- Numerator:
\[ \frac{57}{57} = 1 \]
- Denominator:
\[ \frac{1016}{57} = 17.84 \text{ (approximately)} \]

Thus, the final answer is:
\[ \frac{1}{17.84} \text{ (approximately)} \]

### Final Answer
The final simplified result is approximately:
\[ \frac{1}{17.84} \]