Problem 106 - Introductory Algebra for College Students

Question

If you are given two different real numbers, explain how to determine which one is the lesser.

Step-by-Step Solution

Answer

To determine which of two real numbers is lesser, simply compare them. The number which is closer to zero on the positive side or farthest from zero on the negative side is considered lesser. For example, in the pair (3, 5), 3 is lesser and in the pair (-3, -5), -5 is lesser.

Step 1 Identify the Numbers

The problem begins with two different real numbers. Identify these numbers, and it is important to underscore that these can include both positive and negative numbers, or zero. For example, let's consider two numbers, say, 3 and 5.

Step 2 Comparison

Compare the two numbers. In the realm of reality, if a number is closer to zero or towards the left side of the number line, it is smaller. Hence, 3 is lesser than 5.

Step 3 Consider Negative Numbers

For negative numbers, the rule reverses. The number which is farther from zero is considered as smaller. For example, if we compare -3 and -5, -5 is considered as smaller because it is farther from zero.