To determine which of the fractions can be represented as terminating decimals, we can follow these steps:

Condition for a fraction to be a terminating decimal: A fraction in its simplest form can only be expressed as a terminating decimal if the denominator has no prime factors other than 2 or 5. In other words, when a fraction is reduced to its lowest terms, the denominator should only contain factors of 2 and/or 5.

Let's analyze each fraction in the image:

1. $\frac{1}{16}$:

   • Denominator: 16 = $2^4$
   • Since 16 is a power of 2, $\frac{1}{16}$ is a terminating decimal.

2. $\frac{1}{6}$:

   • Denominator: 6 = $2 \times 3$
   • The denominator contains 3, which is not a factor of 2 or 5. Therefore, $\frac{1}{6}$ is not a terminating decimal.

3. $\frac{6}{32}$:

   • Simplify $\frac{6}{32}$ to $\frac{3}{16}$
   • Denominator: 16 = $2^4$
   • Since 16 is a power of 2, $\frac{3}{16}$ is a terminating decimal.

4. $\frac{3}{11}$:

   • Denominator: 11 (prime number)
   • 11 is not a factor of 2 or 5. Therefore, $\frac{3}{11}$ is not a terminating decimal.

5. $\frac{11}{20}$:

   • Denominator: 20 = $2^2 \times 5$
   • Since the only prime factors of 20 are 2 and 5, $\frac{11}{20}$ is a terminating decimal.

6. $\frac{2}{3}$:

   • Denominator: 3 (prime number)
   • 3 is not a factor of 2 or 5. Therefore, $\frac{2}{3}$ is not a terminating decimal.

The fractions that can be represented as terminating decimals are:

• $\frac{1}{16}$
• $\frac{6}{32}$ (simplified to $\frac{3}{16}$)
• $\frac{11}{20}$

Would you like further details or have any other questions?

Here are some follow-up questions to deepen your understanding:

1. What is the significance of factors 2 and 5 in determining terminating decimals?
2. How can you quickly simplify fractions to identify terminating decimals?
3. Why are prime factors like 3, 11, or other primes problematic for terminating decimals?
4. Can you think of other examples of fractions that yield terminating decimals?
5. How do improper fractions affect the determination of whether a decimal terminates or repeats?

Tip: Always simplify fractions first when analyzing whether they can become terminating decimals!