`(17xx4+4^(2)xx2)/(90div5xx12)=?`

Options

A. `(25)/(54)`
B. `(22)/(57)`
C. `(11)/(27)`
D. `(13)/(27)`

Explanation

To solve the expression \((17 \times 4 + 4^2 \times 2) / (90 \div 5 \times 12)\), we can break it down step by step.

### Step 1: Simplify the numerator
The numerator is \(17 \times 4 + 4^2 \times 2\).

1. Calculate \(17 \times 4\):
\[ 17 \times 4 = 68 \]

2. Calculate \(4^2\):
\[ 4^2 = 16 \]

3. Now calculate \(4^2 \times 2\):
\[ 16 \times 2 = 32 \]

4. Add the results from steps 1 and 3:
\[ 68 + 32 = 100 \]

### Step 2: Simplify the denominator
The denominator is \(90 \div 5 \times 12\).

1. Calculate \(90 \div 5\):
\[ 90 \div 5 = 18 \]

2. Now calculate \(18 \times 12\):
\[ 18 \times 12 = 216 \]

### Step 3: Combine the results
Now we can combine the simplified numerator and denominator:
\[ \frac{100}{216} \]

### Step 4: Simplify the fraction
To simplify \(\frac{100}{216}\), we can find the greatest common divisor (GCD) of 100 and 216.

1. The GCD of 100 and 216 is 4.

2. Divide both the numerator and the denominator by their GCD:
\[ \frac{100 \div 4}{216 \div 4} = \frac{25}{54} \]

### Final Answer
Thus, the final answer is:
\[ \frac{25}{54} \]

---