Problem 13 - Elementary and Intermediate Algebra

Question

Add using the number line. \(-3+(-5)\)

Step-by-Step Solution

Answer

-8

Step 1: Identify the starting point

Begin at the number -3 on the number line.

Step 2: Understand the operation

Since we are adding a negative number -5, this means we will move to the left on the number line.

Step 3: Make the moves

Start at -3. Move 5 units to the left: -4, -5, -6, -7, -8.

Step 4: Determine the result

After moving 5 units to the left, you land on -8.

Key Concepts

number line

The number line is a visual tool that helps us understand numbers and their relationships. Picture a horizontal line with numbers placed at equal intervals. Zero is at the center, positive numbers extend to the right, and negative numbers stretch to the left.

When adding numbers, we use the number line to show our movement. Each step to the right represents adding a positive number, and each step to the left signifies adding a negative number.
For example, if we need to add -3 and -5, we start at -3 on the number line. Then, we move 5 steps to the left because we are adding a negative number (-5). We land on -8.

integers

Integers are the set of whole numbers and their negative counterparts. This includes {..., -3, -2, -1, 0, 1, 2, 3, ...}. They do not have fractions or decimals, making them easy to locate on a number line.

When working with integers, it’s important to understand their properties and how they behave in operations like addition.

• Negative integers are less than zero and found to the left of zero on the number line.
• Positive integers are greater than zero and appear to the right of zero.
• Zero is neutral, not positive nor negative.

Using these properties, we can perform operations such as addition by visualizing movements on the number line.

addition

Addition is the process of combining two or more numbers to get a total. When adding integers, the number line can be extremely helpful.

Here are some steps to help you add integers:

• Identify the starting point: Begin at the first number on the number line.
• Understand the operation: Determine if you are adding a positive or negative number. This informs your direction on the number line.
• Make the moves: Move the number of steps corresponding to the integer being added. Right for positive, left for negative.
• Determine the result: The point where you land is your answer.

Following these steps can make adding integers, even negative ones, straightforward and intuitive.