Let's analyze the number [tex]\(-\frac{2}{5}\)[/tex].
### Step-by-Step Analysis:
1. Integer:
- Definition: An integer is any whole number, positive, negative, or zero.
- Analysis: [tex]\(-\frac{2}{5}\)[/tex] is a fraction, not a whole number. Therefore, it is not an integer.
2. Whole:
- Definition: Whole numbers are non-negative integers, including zero (0, 1, 2, 3, ...).
- Analysis: Since whole numbers are non-negative integers and [tex]\(-\frac{2}{5}\)[/tex] is negative and a fraction, it is not a whole number.
3. Natural:
- Definition: Natural numbers are positive integers (1, 2, 3, ...).
- Analysis: Since natural numbers are positive and [tex]\(-\frac{2}{5}\)[/tex] is not a positive integer (it's not an integer at all and it's negative), it is not a natural number.
4. Rational:
- Definition: A rational number is any number that can be expressed as the quotient or fraction [tex]\(\frac{p}{q}\)[/tex], where [tex]\(p\)[/tex] and [tex]\(q\)[/tex] are integers and [tex]\(q \neq 0\)[/tex].
- Analysis: [tex]\(-\frac{2}{5}\)[/tex] is expressed as a fraction [tex]\(\frac{a}{b}\)[/tex] with [tex]\(a = -2\)[/tex] and [tex]\(b = 5\)[/tex], which are both integers and [tex]\(b \neq 0\)[/tex]. Hence, [tex]\(-\frac{2}{5}\)[/tex] is a rational number.
### Conclusion:
Based on the analysis, [tex]\(-\frac{2}{5}\)[/tex] is only a rational number.
Thus, the types of number [tex]\(-\frac{2}{5}\)[/tex] is:
- Rational
