Question

Which set includes rational numbers but not natural numbers?

A. -6 2/3, -2, 5/11, 7/8
B. 0, 1, 2, 3
C. 3/4, 4 5/6, 18/5, 8
D. -5, -4, 4, 5

Answer 1

To determine which set includes rational numbers but not natural numbers, let's first define the two types of numbers:

- **Natural Numbers**: These are the numbers starting from 1 and going upwards (1, 2, 3, ...). They do not include 0 or negative numbers.
- **Rational Numbers**: These are numbers that can be expressed as a fraction, where both the numerator and denominator are integers (and the denominator is not zero).

Now, let's analyze each option:

**A. -6 2/3, -2, 5/11, 7/8**
- All of these numbers are rational (they can all be expressed as fractions).
- However, they do not include any natural numbers.

**B. 0, 1, 2, 3**
- All of these numbers are natural numbers (starting from 1).
- 0 is not a natural number, but it is not included in the aspect of the problem since we need to find a set that does not contain natural numbers at all.

**C. 3/4, 4 5/6, 18/5, 8**
- Here, 3/4, 4 5/6, and 18/5 are all rational numbers.
- The number 8 is also a rational number and a natural number since it is positive whole number.

**D. -5, -4, 4, 5**
- The numbers -5 and -4 are rational and do not belong to natural numbers.
- The numbers 4 and 5, however, are natural numbers.

From this analysis, option **A** is the set that includes only rational numbers without any natural numbers. Therefore, the answer is:

**A. -6 2/3, -2, 5/11, 7/8**.