Choose all of the rational numbers. \[ \square \frac{-5}{0} \quad \square \frac{0}{0} \quad \square 0.11 \overline{1} \quad \square \frac{0}{-10} \quad \square \sqrt{2} \quad \square \frac{2}{-2} \quad \square \sqrt{36} \]

To determine which of the given expressions are rational numbers, let's analyze each one: 1. **\(\frac{-5}{0}\)** - **Undefined**: Division by zero is not defined in mathematics. - **Not a rational number**. 2. **\(\frac{0}{0}\)** - **Undefined**: This expression is indeterminate and has no defined value. - **Not a rational number**. 3. **\(0.11\overline{1}\)** - **Repeating Decimal**: This represents the number \(0.1111\ldots\), which is equal to \(\frac{1}{9}\). - **Rational number**. 4. **\(\frac{0}{-10}\)** - **Simplifies to 0**: Any number divided by a non-zero number is 0. - **Rational number**. 5. **\(\sqrt{2}\)** - **Irrational Number**: \(\sqrt{2}\) cannot be expressed as a fraction of two integers. - **Not a rational number**. 6. **\(\frac{2}{-2}\)** - **Simplifies to -1**: This is a simple division resulting in -1. - **Rational number**. 7. **\(\sqrt{36}\)** - **Simplifies to 6**: Since \(\sqrt{36} = 6\), which is an integer. - **Rational number**. **Rational Numbers from the List:** - \(0.11\overline{1}\) - \(\frac{0}{-10}\) - \(\frac{2}{-2}\) - \(\sqrt{36}\) **Therefore, the rational numbers are:** - \(0.11\overline{1}\) - \(\frac{0}{-10}\) - \(\frac{2}{-2}\) - \(\sqrt{36}\)