Certainly! Let's explore how to determine if the real number [tex]\(-6\)[/tex] can be classified as a rational number.
### Definition of a Rational Number:
A real number is considered rational if it can be expressed as the quotient of two integers [tex]\(\frac{a}{b}\)[/tex], where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are integers and [tex]\(b \neq 0\)[/tex].
### Step-by-Step Solution:
1. Identify the given number: The number in question is [tex]\(-6\)[/tex].
2. Express [tex]\(-6\)[/tex] as a quotient:
- [tex]\(-6\)[/tex] can be expressed as [tex]\(\frac{-6}{1}\)[/tex], where [tex]\(-6\)[/tex] is an integer and 1 is also an integer.
- The denominator [tex]\(1\)[/tex] is not zero, which satisfies the condition for a rational number.
3. Conclusion:
- Since [tex]\(-6\)[/tex] can be expressed as [tex]\(\frac{-6}{1}\)[/tex], it fulfills the criterion of being a rational number.
Hence, we can conclude that the real number [tex]\(-6\)[/tex] is a rational number.
Answer:
- True
This detailed explanation confirms that [tex]\(-6\)[/tex] is a rational number because it meets all the necessary conditions.
