Problem 40 - Introductory Algebra for College Students

Question

Give an example of a rational number that is not a natural number.

Step-by-Step Solution

Answer

One example of a rational number that is not a natural number would be -2.

Step 1: Understanding the Different Number Types

Get to know what natural numbers and rational numbers are. Natural numbers are all positive whole numbers starting from 1. Rational numbers encompass all numbers that can be written as a quotient of two integers. Fractional numbers or whole integers, both positive and negative, as well as zero, are included in the set of rational numbers.

Step 2: Comparing the Definitions

Compare the definitions of the two sets of numbers. Rational numbers encompass a much larger set of numbers compared to natural numbers. Therefore, there are rational numbers that are not natural numbers.

Step 3: Finding an Example

Choose an example based on the analysis. Any fraction, negative number, or zero, would qualify. Let's choose \(-2\) as an example. \(-2\) is a rational number because it can be expressed as the quotient of two integers \( \frac{-2}{1}\) and it is not a natural number because it is negative.