1. **State the problem:** Solve for $v$ in the equation $$40 = \frac{8}{5} v$$. 2. **Formula and rules:** To isolate $v$, divide both sides of the equation by the coefficient of $v$, which is $\frac{8}{5}$. Remember, dividing by a fraction is the same as multiplying by its reciprocal. 3. **Isolate $v$:** $$v = \frac{40}{\frac{8}{5}}$$ 4. **Multiply by the reciprocal:** $$v = 40 \times \frac{5}{8}$$ 5. **Simplify the multiplication:** $$v = \cancel{40} \times \frac{5}{\cancel{8}} = 5 \times 5 = 25$$ 6. **Final answer:** $$v = 25$$