1. The problem asks whether the decimal representations of the fractions $\frac{2}{5}$, $\frac{15}{20}$, and $\frac{6}{16}$ will repeat or terminate. 2. A fraction in simplest form will have a terminating decimal if and only if its denominator (after simplification) has only the prime factors 2 and/or 5. 3. Let's simplify each fraction and analyze the denominator: - $\frac{2}{5}$ is already in simplest form. The denominator is 5, which is a prime factor of 5 only. - $\frac{15}{20}$ simplifies to $\frac{3}{4}$ by dividing numerator and denominator by 5. The denominator 4 factors as $2^2$. - $\frac{6}{16}$ simplifies to $\frac{3}{8}$ by dividing numerator and denominator by 2. The denominator 8 factors as $2^3$. 4. Since all denominators after simplification have only 2s and/or 5s as prime factors, all these fractions have terminating decimal representations. 5. To confirm, let's convert each to decimal: - $\frac{2}{5} = 0.4$ - $\frac{15}{20} = \frac{3}{4} = 0.75$ - $\frac{6}{16} = \frac{3}{8} = 0.375$ All decimals terminate. Final answer: All three fractions have terminating decimals.