The value of `(1/2 div 1/2 "of"1/2)/(1/2+1/2 "of"1/2)` is

Options

A. `2//3`
B. 2
C. `8//3`
D. 3

Answer

To solve the expression \((1/2 \div 1/2 \text{ of } 1/2) / (1/2 + 1/2 \text{ of } 1/2)\), we will follow these steps:

### Step 1: Understand the term "of"
In mathematics, "of" typically means multiplication. Therefore, we can rewrite the expression using multiplication.

### Step 2: Rewrite the expression
The expression can be rewritten as:
\[ \frac{1/2 \div (1/2 \times 1/2)}{1/2 + (1/2 \times 1/2)} \]

### Step 3: Calculate \(1/2 \times 1/2\)
Now, we calculate \(1/2 \times 1/2\):
\[ 1/2 \times 1/2 = 1/4 \]

### Step 4: Substitute back into the expression
Substituting \(1/4\) back into the expression gives us:
\[ \frac{1/2 \div 1/4}{1/2 + 1/4} \]

### Step 5: Calculate \(1/2 \div 1/4\)
Next, we calculate \(1/2 \div 1/4\):
\[ 1/2 \div 1/4 = 1/2 \times 4/1 = 2 \]

### Step 6: Calculate \(1/2 + 1/4\)
Now, we calculate \(1/2 + 1/4\). To do this, we need a common denominator:
\[ 1/2 = 2/4 \]
So,
\[ 1/2 + 1/4 = 2/4 + 1/4 = 3/4 \]

### Step 7: Substitute back into the expression
Now we substitute back into the expression:
\[ \frac{2}{3/4} \]

### Step 8: Simplify the fraction
To simplify \(\frac{2}{3/4}\), we multiply by the reciprocal:
\[ 2 \times \frac{4}{3} = \frac{8}{3} \]

### Final Answer
Thus, the value of the expression is:
\[ \frac{8}{3} \]