Choose all of the rational numbers. \( \frac{-5}{0} \) \( \frac{0}{0} \) \( 0.11 \overline{1} \) \( \frac{0}{-10} \) \( \sqrt{2} \) \( \frac{2}{-2} \) \( \sqrt{36} \)

To determine which of the provided numbers are rational, let's evaluate each one: 1. **\(\frac{-5}{0}\)**: Division by zero is undefined, so this is **not** a rational number. 2. **\(\frac{0}{0}\)**: This is an indeterminate form and is **not** a rational number. 3. **\(0.11\overline{1}\)**: - This represents a repeating decimal: \(0.1111\ldots\), which can be expressed as the fraction \(\frac{1}{9}\). - Since it can be written as a ratio of two integers, it **is** a rational number. 4. **\(\frac{0}{-10}\)**: - This simplifies to \(0\). - Zero is a rational number because it can be expressed as \(\frac{0}{1}\). 5. **\(\sqrt{2}\)**: - \(\sqrt{2}\) is an irrational number, meaning it cannot be expressed as a ratio of two integers. 6. **\(\frac{2}{-2}\)**: - This simplifies to \(-1\). - Since \(-1\) is an integer, it **is** a rational number. 7. **\(\sqrt{36}\)**: - \(\sqrt{36} = 6\), which is an integer. - Integers are rational numbers because they can be expressed as a ratio (e.g., \(\frac{6}{1}\)). **Rational Numbers from the List:** - \(0.11\overline{1}\) - \(\frac{0}{-10}\) - \(\frac{2}{-2}\) - \(\sqrt{36}\) **Answer:** All of the following are rational:  \(0.11 \overline{1}\),  \(\frac{0}{-10}\),  \(\frac{2}{-2}\), and  \(\sqrt{36}\).