Question

The value of \(\frac{\frac{1}{2}+\frac{1}{2}\text{of}\frac{1}{2}}{\frac{1}{2}+\frac{1}{2}\text{of}\frac{1}{2}}\)is

• A. \(\frac{2}{3}\)
• B. 2
• C. \(\frac{4}{3}\)
• D. 3

Answer 1

The Correct Option is A

The expression we need to evaluate is \(\frac{\frac{1}{2}+\frac{1}{2}\text{ of }\frac{1}{2}}{\frac{1}{2}+\frac{1}{2}\text{ of }\frac{1}{2}}\). To begin, evaluate the terms involved:

\[\frac{1}{2} \text{ of }\frac{1}{2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\]

Substitute back into the expression:

\[\frac{\frac{1}{2}+\frac{1}{4}}{\frac{1}{2}+\frac{1}{4}}\]

Calculate the numerator and the denominator:

Numerator: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\)

Denominator: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\)

This simplifies the expression to:

\[\frac{\frac{3}{4}}{\frac{3}{4}} = 1\]

Therefore, the initial problem appears to have an issue because the structure of the numbered answer (\(\frac{2}{3}\)) does not equate with the calculation result. Please reassess the problem structure to align with the provided answer structure correctly.