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

Options

A. 1
B. `1 (1)/(3)`
C. `2(2)/(3)`
D. 3

Answer

To solve the expression \(\frac{\frac{1}{2} - \left(\frac{1}{2} \text{ of } \frac{1}{2}\right)}{\frac{1}{2} + \left(\frac{1}{2} \text{ of } \frac{1}{2}\right)}\), we will follow these steps:

### Step 1: Simplify the "of" operation
The term \(\frac{1}{2} \text{ of } \frac{1}{2}\) can be simplified as:
\[ \frac{1}{2} \text{ of } \frac{1}{2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]

### Step 2: Substitute back into the expression
Now we substitute \(\frac{1}{4}\) back into the original expression:
\[ \frac{\frac{1}{2} - \frac{1}{4}}{\frac{1}{2} + \frac{1}{4}} \]

### Step 3: Simplify the numerator
For the numerator:
\[ \frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4} \]

### Step 4: Simplify the denominator
For the denominator:
\[ \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \]

### Step 5: Form the new fraction
Now we have:
\[ \frac{\frac{1}{4}}{\frac{3}{4}} \]

### Step 6: Simplify the fraction
To simplify \(\frac{\frac{1}{4}}{\frac{3}{4}}\), we multiply by the reciprocal of the denominator:
\[ \frac{1}{4} \times \frac{4}{3} = \frac{1}{3} \]

### Final Answer
Thus, the value of the expression is:
\[ \frac{1}{3} \]

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