1. **State the problem:** Multiply the fractions $\frac{2}{7}$ and $\frac{14}{16}$. 2. **Formula:** To multiply fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. **Apply the formula:** $$\frac{2}{7} \times \frac{14}{16} = \frac{2 \times 14}{7 \times 16} = \frac{28}{112}$$ 4. **Simplify the fraction:** Find the greatest common divisor (GCD) of 28 and 112, which is 28. $$\frac{\cancel{28}^{1}}{\cancel{112}^{4}} = \frac{1}{4}$$ 5. **Final answer:** $$\frac{2}{7} \times \frac{14}{16} = \frac{1}{4}$$