`(1/2div4+20)/(1/2xx4+20)=?`

Options

A. (31/88)
B. (2)3/11
C. (161/176)
D. 1

Answer

To solve the expression \((\frac{1}{2} \div 4 + 20) / (\frac{1}{2} \times 4 + 20)\), we will follow these steps:

### Step 1: Simplify the numerator
The numerator is \(\frac{1}{2} \div 4 + 20\).
- First, we need to perform the division:
\[ \frac{1}{2} \div 4 = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \]
- Now, add 20:
\[ \frac{1}{8} + 20 = \frac{1}{8} + \frac{160}{8} = \frac{161}{8} \]

### Step 2: Simplify the denominator
The denominator is \(\frac{1}{2} \times 4 + 20\).
- First, we perform the multiplication:
\[ \frac{1}{2} \times 4 = 2 \]
- Now, add 20:
\[ 2 + 20 = 22 \]

### Step 3: Combine the results
Now we have:
\[ \frac{\frac{161}{8}}{22} \]
- To simplify this, we can rewrite it as:
\[ \frac{161}{8} \div 22 = \frac{161}{8} \times \frac{1}{22} = \frac{161}{176} \]

### Step 4: Simplify the fraction
Now, we check if \(\frac{161}{176}\) can be simplified. The greatest common divisor (GCD) of 161 and 176 is 1, so it cannot be simplified further.

Thus, the final answer is:
\[ \frac{161}{176} \]