`(16)/(23) xx ( 47)/( 288) xx ( 92)/( 141) = ?`

Options

A. `(4)/( 27)`
B. `( 2)/( 27)`
C. `( 2)/( 29)`
D. `( 3)/( 28)`

Answer

To solve the problem \((16/23) \times (47/288) \times (92/141)\), we will follow these steps:

### Step 1: Write the expression clearly
We start with the expression:
\[ \frac{16}{23} \times \frac{47}{288} \times \frac{92}{141} \]

### Step 2: Multiply the numerators and denominators
We can multiply the numerators together and the denominators together:
\[ \frac{16 \times 47 \times 92}{23 \times 288 \times 141} \]

### Step 3: Simplify the fractions
Now we will simplify the fractions step by step.

#### Step 3.1: Simplify \(92\) and \(23\)
Notice that \(92\) can be divided by \(23\):
\[ 92 \div 23 = 4 \quad \text{(since \(23 \times 4 = 92\))} \]
So, we can rewrite the expression:
\[ \frac{16 \times 47 \times 4}{1 \times 288 \times 141} \]

#### Step 3.2: Simplify \(16\) and \(288\)
Next, we can simplify \(16\) and \(288\):
\[ 288 \div 16 = 18 \quad \text{(since \(16 \times 18 = 288\))} \]
So, we rewrite the expression:
\[ \frac{1 \times 47 \times 4}{1 \times 18 \times 141} \]

#### Step 3.3: Simplify \(47\) and \(141\)
Next, we simplify \(47\) and \(141\):
\[ 141 \div 47 = 3 \quad \text{(since \(47 \times 3 = 141\))} \]
So, we rewrite the expression:
\[ \frac{1 \times 1 \times 4}{1 \times 18 \times 3} \]

### Step 4: Final multiplication
Now we have:
\[ \frac{4}{54} \]
We can simplify this further:
\[ \frac{4}{54} = \frac{2}{27} \quad \text{(dividing both numerator and denominator by 2)} \]

### Final Answer
Thus, the final answer is:
\[ \frac{2}{27} \]

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