Sure, let's go through each of the given statements to determine which one accurately describes a rational number.
A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. This means it can take various forms, including both integers and fractions. Let's analyze each statement one by one:
1. A rational number can be a fraction that is not a whole number.
- Yes, this is true. Rational numbers include fractions such as [tex]\(\frac{1}{2}\)[/tex], which are not whole numbers. This means they can be expressed as non-whole number fractions.
2. Must be positive.
- This is false. Rational numbers include both positive and negative numbers as long as they can be expressed as the ratio of two integers. For example, [tex]\(-\frac{3}{4}\)[/tex] is also a rational number.
3. Cannot be a whole number.
- This statement is false as well. Whole numbers like 3 can be expressed as [tex]\(\frac{3}{1}\)[/tex], and thus are also considered rational numbers. Hence, rational numbers can indeed be whole numbers.
4. Is always an integer.
- This is false. Rational numbers include fractions, which are not integers. For instance, [tex]\(\frac{2}{3}\)[/tex] is a rational number but not an integer.
Given all these considerations, the statement "A rational number can be a fraction that is not a whole number" is the correct one. Therefore, the correct answer is:
1. A rational number can be a fraction that is not a whole number.
