To determine which of the given numbers are rational, we need to recall that a rational number can be expressed as a fraction of two integers (where the denominator is not zero). Let's evaluate each option:

A. $\frac{1}{7}$ - This is a fraction of two integers, so it is rational.

B. $\frac{\pi}{2}$ - This involves $\pi$, which is an irrational number. Hence, $\frac{\pi}{2}$ is also irrational.

C. $\sqrt{13}$ - The square root of 13 is not an integer and cannot be expressed as a fraction of two integers. Therefore, it is irrational.

D. $9 \frac{2}{3}$ - This is a mixed number which can be converted to an improper fraction ($\frac{29}{3}$), thus it is rational.

E. $2 \sqrt{10}$ - The square root of 10 is irrational, and multiplying it by 2 does not change its irrationality.

From the analysis, the rational numbers are:

• Option A: $\frac{1}{7}$
• Option D: $9 \frac{2}{3}$ (or $\frac{29}{3}$)

Do you have any questions or need further details?

Here are five related questions to expand your understanding:

1. What makes a number irrational?
2. Can the product of a rational and an irrational number ever be rational?
3. How can you convert a mixed number to an improper fraction?
4. What are some examples of numbers that are always irrational?
5. How can you determine if a given square root is rational or irrational?

Tip: A rational number is any number that can be written as a fraction, where both the numerator and the denominator are integers, and the denominator is not zero.