Problem 39 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

An example of a rational number that is not an integer is \(\frac{1}{2}\). This number satisfies all the conditions of being a rational number, i.e., it is the ratio of two integers where the denominator is not zero. However, it is not an integer because it is not a whole number.

Step 1: Definition of Rational Numbers and Integers

A rational number is a number that can be expressed as a division or fraction of two integers. The numerator is an integer and the denominator is an integer, but the denominator cannot be zero. An integer on the other hand is any whole number, including zero, and its additive inverse (negative).

Step 2: Finding a Non-Integer Rational Number

To find a rational number that is not an integer, we look for a number that is not a whole number, i.e., it must have a decimal or fractional part. Therefore, we could select a simple fraction where the denominator is not 1 or -1 because any integer divided by 1 or -1 always results in an integer. Let's choose, for instance, the fraction \(\frac{1}{2}\).