1. The problem is to evaluate the expressions $2\left(\frac{7}{3}\right)$ and $\frac{1}{2}\left(\frac{8}{3}\right)$. 2. Recall the rule for multiplying a whole number or fraction by a fraction: multiply the numerator by the outside number and keep the denominator the same. 3. For the first expression: $$2\left(\frac{7}{3}\right) = \frac{2 \times 7}{3} = \frac{14}{3}$$ 4. For the second expression: $$\frac{1}{2}\left(\frac{8}{3}\right) = \frac{1 \times 8}{2 \times 3} = \frac{8}{6} = \frac{4}{3}$$ 5. So the evaluated expressions are $\frac{14}{3}$ and $\frac{4}{3}$ respectively. 6. These are simplified fractions representing the final answers.