Problem 8 - Introductory and Intermediate Algebra for College Students 4th

Question

Find each sum using a number line. $$5+(-5)$$

Step-by-Step Solution

Answer

The sum of 5 and -5 using a number line is 0.

Step 1: Understanding positive and negative movements on the Number Line

Positive numbers represent a rightward movement along the number line, while negative numbers represent a leftward movement. In this case, +5 represents a move 5 steps to the right from 0.

Step 2: Adding Positive Integer on Number Line

Start at 0 on the number line, and move 5 steps to the right. The position on the number line after this step is 5.

Step 3: Adding Negative Integer on Number Line

Now, from the position 5 on number line, move 5 steps to the left (which is represented by -5). You will land at 0.

Key Concepts

Positive Numbers

Positive numbers are those greater than zero. On a number line, these are always marked to the right of the origin (which is zero). When you are adding a positive number, you move to the right. It means increasing or augmenting the value.

• To visualize with a number line: if you start at 0, adding the positive number 5 means moving 5 steps to the right, landing on 5.
• This movement signifies an increase, as you are moving towards larger numbers or a positive direction.

Remember, the further right you go, the larger the value becomes, indicating increasing quantities or value.

Negative Numbers

Negative numbers are less than zero, displayed to the left of the origin on a number line. They indicate a decrease or subtraction when added to another number. Moving left is the key action when dealing with negative numbers.

• If you start from a positive number, like 5, and add -5, you move 5 steps to the left on the number line, ending back at 0.
• This represents a reduction or decrease in value, as moving left decreases the magnitude.

In essence, negative numbers counteract positive movements, bringing values down or moving left on the line.

Integer Addition

Integer addition involves combining whole numbers, which could be either positive or negative, using a number line to aid visualization.

• The key is direction: moving right for positive numbers and left for negative numbers.
• Consider the example: adding 5 and -5 on a number line involves moving right 5 steps from 0 and then left 5 steps, returning to 0.

The outcome shows that adding opposite integers, like 5 and -5, results in a total of zero, illustrating how positive and negative actions can balance out each other.