Question: 3 \times \left|\left| \frac{7}{2} \right|\right|
1. **State the problem:** Calculate the product of $3$ and the absolute value of $\frac{7}{2}$.
2. **Recall the absolute value rule:** The absolute value of a number is its distance from zero on the number line, always non-negative. For a positive fraction like $\frac{7}{2}$, the absolute value is the number itself.
3. **Calculate the absolute value:**
$$\left|\frac{7}{2}\right| = \frac{7}{2}$$
4. **Multiply:**
$$3 \times \frac{7}{2} = \frac{3 \times 7}{2} = \frac{21}{2}$$
5. **Simplify if needed:**
The fraction $\frac{21}{2}$ is already in simplest form.
**Final answer:**
$$\boxed{\frac{21}{2}}$$