Yes, some rational numbers are natural numbers.
Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0. Natural numbers are positive integers (1, 2, 3, ...). Since any natural number n can be written as n/1, it fits the definition of a rational number. Therefore, all natural numbers are also rational numbers. However, not all rational numbers are natural numbers (e.g., 1/2, -3/4).
Explanation:
- Rational Numbers: Any number that can be expressed in the form p/q, where p and q are integers (whole numbers) and q is not zero. Examples: 2/3, 5/1, -7/2, 0.
- Natural Numbers: Positive whole numbers starting from 1. Examples: 1, 2, 3, 4, 5...
- Relationship: Natural numbers are a subset of rational numbers because any natural number n can be expressed as the rational number n/1.
Examples:
- 5 is a natural number. It is also a rational number because it can be expressed as 5/1.
- 100 is a natural number and also a rational number (100/1).
- 0.5 (or 1/2) is a rational number but not a natural number.
- -3 is a rational number (-3/1) but not a natural number.
Table summarizing the relationship:
| Number | Natural Number? | Rational Number? |
|---|---|---|
| 5 | Yes | Yes |
| 1/2 | No | Yes |
| -3 | No | Yes |
| 0 | No | Yes (0/1) |
In conclusion, while all natural numbers are rational numbers, the reverse is not true. Many rational numbers (like fractions and negative numbers) do not fall within the set of natural numbers.
