Question

Describe the set of numbers that are real numbers but cannot be expressed as one integer divided by another.

Irrational
Improper
Negative
rational

Answer 1

The set of numbers that are real numbers but cannot be expressed as one integer divided by another are called **irrational numbers**.

To clarify the options:

- **Irrational**: These are numbers that cannot be expressed as a fraction of two integers (i.e., cannot be written in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \)). Examples include numbers like \( \pi \) and \( \sqrt{2} \).

- **Improper**: In the context of fractions, an improper fraction is one where the numerator is greater than or equal to the denominator (e.g., \( \frac{5}{4} \)). This term does not relate to the set of non-rational numbers.

- **Negative**: This term refers to numbers less than zero, but it does not specifically denote whether a number is rational or irrational.

- **Rational**: These are numbers that can be expressed as the fraction of two integers (e.g., \( \frac{1}{2} \), \( \frac{3}{4} \)), so they do not fit the description given.

Thus, the correct answer is **irrational** numbers.