The table asks you to classify numbers as rational or irrational by marking the appropriate category. Upon reviewing the provided answers:

1. $\frac{31}{\sqrt{6}}$:

   • $\sqrt{6}$ is an irrational number, so dividing 31 by it will result in an irrational number.
   • Correct answer: Check under "Irrational."

2. $-11$:

   • $-11$ is an integer and can be expressed as $\frac{-11}{1}$, which is a rational number.
   • Correct answer: Check under "Rational."

3. $\pi$:

   • $\pi$ is a well-known irrational number.
   • Correct answer: Check under "Irrational."

4. $\frac{3}{8}$:

   • This is a fraction of two integers, which makes it a rational number.
   • Correct answer: Check under "Rational."

5. $\sqrt{20}$:

   • Simplify $\sqrt{20}$ to $2\sqrt{5}$, where $\sqrt{5}$ is irrational. Hence, $\sqrt{20}$ is also irrational.
   • Correct answer: Check under "Irrational."

Corrected Table

Let me know if you’d like a breakdown of any specific number or a further explanation!

Follow-Up Questions:

1. How is a number like $\pi$ classified as irrational?
2. Can $\sqrt{6}$ be represented as a rational number?
3. What distinguishes repeating decimals from non-repeating decimals in this context?
4. Why is dividing by an irrational number (like $\sqrt{6}$) significant?
5. Are all square roots of non-perfect squares irrational?

Tip: Remember, if a number can be written as a fraction $\frac{p}{q}$ (where $p$ and $q$ are integers), it’s rational! Otherwise, it’s irrational.