Problem 85 - Introductory Algebra for College Students

Question

Without using a number line, describe how to add two numbers with different signs. Give an example.

Step-by-Step Solution

Answer

The method to add two numbers with different signs is to subtract the absolute value of the smaller number from the absolute value of the larger number, and then assign the sign of the number with the larger absolute value. For example, adding -5 and 3 would result in -2.

Step 1: Understanding the Concept

First, it is important to understand what the signs represent when it comes to numbers. In terms of temperature, for example, positive numbers indicate degrees above zero while negative numbers indicate degrees below zero. Here, the goal is to understand the concept of absolute value which is the numerical value of a real number without regard to its sign.

Step 2: Rule of Adding Different Signs

The rule for adding two numbers with different signs is to take the difference of their absolute values (or subtract the lesser absolute value from the greater absolute value) and then keep the sign of the number with the larger absolute value. It is essentially the subtraction operation.

Step 3: Apply the Rule with an Example

Taking an example of two numbers -5 and 3. The absolute value of -5 is 5, and the absolute value of 3 is 3. Subtracing 3 from 5 gives 2. As the number with the larger absolute value is -5, the result will be -2. So, -5 added to 3 results in -2.