Question

Which set includes rational numbers but not natural numbers?

(1 point)
Responses

3/4, 4 5/6, 18/5, 8

0, 1, 2, 3

−5, −4, 4, 5

−6 2/3, −2, 5/11, 7/8

Answer 1

To identify the set that includes rational numbers but not natural numbers, we first need to understand the definitions:

- **Natural numbers** are the set of positive integers (1, 2, 3, ...) and sometimes include 0.
- **Rational numbers** include fractions and numbers that can be expressed as the quotient of two integers.

Now, let’s analyze each option:

1. **3/4, 4 5/6, 18/5, 8**:
- This set contains rational numbers, but also the natural number 8.

2. **0, 1, 2, 3**:
- This set contains the natural numbers (1, 2, 3) and also includes 0, but 0 is not a natural number if we only consider positive natural numbers.
- However, since it contains some natural numbers, it doesn't fit the criteria.

3. **−5, −4, 4, 5**:
- This set contains rational numbers, including the natural number 4 and the positive integer 5.
- Thus, it does not meet the requirement.

4. **−6 2/3, −2, 5/11, 7/8**:
- This set includes negative rational numbers (−6 2/3, −2) and positive rational numbers (5/11, 7/8).
- None of these numbers are natural numbers.

Based on the analysis, the correct response is:

**−6 2/3, −2, 5/11, 7/8**