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Chapter 1: Problem 8

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

Short Answer

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

Step by step solution

01

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.
02

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.
03

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

Exercises \(150-152\) will help you prepare for the material covered in the next section. In each exercise, an expression with an exponent is written as a repeated multiplication. Find this product, indicated by a question mark. $$(-6)^{2}=(-6)(-6)=?$$

Why is it that 0 has no multiplicative inverse?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some whole numbers are not integers.

In each exercise, determine whether the given number is a solution of the equation. $$4 x+2=3(x-6)+8 ;-11$$

Find this sum, indicated by a question mark. \(3(-3)=(-3)+(-3)+(-3)=?\)
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