1. **State the problem:** Simplify the expression $v - \frac{v}{3}$. 2. **Write the expression with a common denominator:** To combine the terms, express $v$ as $\frac{3v}{3}$. $$v - \frac{v}{3} = \frac{3v}{3} - \frac{v}{3}$$ 3. **Combine the fractions:** Since the denominators are the same, subtract the numerators. $$\frac{3v}{3} - \frac{v}{3} = \frac{3v - v}{3}$$ 4. **Simplify the numerator:** $$\frac{3v - v}{3} = \frac{2v}{3}$$ 5. **Final answer:** The simplified form of $v - \frac{v}{3}$ is $$\boxed{\frac{2v}{3}}$$