Final answer:
The number -8 does not belong to the Natural numbers or Whole numbers because it is negative. However, it belongs to the Integers as it is a whole number and its opposite, and it is also a Rational number since it can be written as a fraction -8/1.
Step-by-step explanation:
To determine which set(s) the number -8 belongs to, we need to understand the definitions of each of the sets mentioned in the question.
- Natural numbers: These are the set of positive integers beginning from 1 (1, 2, 3, ...). Since -8 is a negative number, it does not belong to the natural numbers.
- Whole numbers: These include all the natural numbers along with 0 (0, 1, 2, 3, ...). Just like natural numbers, whole numbers do not include negative numbers, so -8 is not a whole number.
- Integers: This set consists of all whole numbers and their opposites (..., -3, -2, -1, 0, 1, 2, 3, ...). Since -8 is an opposite of 8, which is a whole number, -8 falls under the category of integers.
- Rational numbers: These are numbers that can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. -8 can be written as -8/1, making it a rational number as well.
Therefore, the number -8 belongs to the sets of Integers and Rational numbers.