Problem 84 - Introductory Algebra for College Students

Question

Without using a number line, describe how to add two numbers with the same sign. Give an example.

Step-by-Step Solution

Answer

To add numbers with the same sign, directly add the absolute values of the numbers and keep the shared sign. For example, 5 + 7 = 12 and -4 - 6 = -10.

Step 1: Understand Concept

Understand that when two numbers of the same sign are added together, the result keeps the same sign. If they are two positive numbers, the result is positive. If they are two negative numbers, the result is negative.

Step 2: Application of Concept

Consider two positive numbers, for example, 5 and 7. Since both numbers are positive, their sum would also be positive. You should directly add the numbers to each other, disregarding the sign, then place the shared sign at the beginning of the result. In this case: 5 + 7 = 12.

Step 3: Application of Concept to Negative Numbers

Now let's consider two negative numbers, for example, -4 and -6. Since both numbers are negative, their sum would also be negative. Subtract the smaller absolute magnitude from the larger, then place a negative sign at the beginning of the result. In this case: -4 -6 = -10.