`(2)/(3)` of three-fourth of a number is :

Options

A. `(1)/(2)`
B. `(1)/(3)`
C. `(8)/(9)`
D. `(17)/(12)`

Answer

To solve the problem, we need to find \(\frac{2}{3}\) of \(\frac{3}{4}\) of a number. Let's denote the unknown number as \(x\).

### Step-by-step Solution:

1. **Identify the expression**: We need to find \(\frac{2}{3}\) of \(\frac{3}{4}\) of \(x\). This can be expressed mathematically as:
\[ \frac{2}{3} \times \frac{3}{4} \times x \]

2. **Multiply the fractions**: First, we multiply \(\frac{2}{3}\) and \(\frac{3}{4}\):
\[ \frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12} \]

3. **Simplify the fraction**: Now, simplify \(\frac{6}{12}\):
\[ \frac{6}{12} = \frac{1}{2} \]

4. **Express the final result**: Now, we can express the result in terms of \(x\):
\[ \frac{1}{2} \times x \]

5. **Conclusion**: Therefore, \(\frac{2}{3}\) of \(\frac{3}{4}\) of a number \(x\) is:
\[ \frac{x}{2} \]

### Final Answer:
The answer is \(\frac{x}{2}\).