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Chapter 1: Problem 24

Add. Do not use the number line except as a check. \(-18+18\)

Short Answer

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Step by step solution

01

Identify the Numbers

The equation to solve is \( -18 + 18 \). Notice that one number is negative and the other one is positive.
02

Understand Opposites

Understand that \( -18 \) and \( 18 \) are opposites. When you add a number to its opposite, the sum is always zero.
03

Perform the Addition

Since \( -18 + 18 \) are opposites, their sum is \( 0 \). Therefore, \( -18 + 18 = 0 \).
04

Check Using Number Line (Optional)

To check, you could use a number line: start at -18 and move 18 steps to the right. 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.

opposites in mathematics
In mathematics, opposites are pairs of numbers that, when added together, equal zero.
These numbers are often called additive inverses.
The basic idea is that for any number, there exists another number such that their sum is zero.
For example:
  • -18 and 18
  • -5 and 5
  • -100 and 100
These pairs are opposites.
The relationship between opposites is fundamental in integer addition.
By recognizing that one number is the exact negative of another, you can easily solve addition problems.
sum of opposites
The sum of opposites always equals zero.
This concept is important in understanding how integers work together.
When you add a number to its opposite, no matter how large or small, the result is zero.
Consider the equation \(-18 + 18\):
  • -18 is the opposite of 18
  • By adding them, you perform the operation: \(-18 + 18 = 0\)
The result is zero because the negative value cancels out the positive value.
This principle helps simplify many arithmetic problems.
zero property of addition
The zero property of addition states that any number added to its opposite will equal zero.
This property is based on the basic rules of arithmetic and integer operations.
Let's break it down:
  • Every integer has an opposite (or additive inverse).
  • When a number and its opposite are added, they cancel each other out.
  • The result is always zero.
For example, \(-18 + 18\ = 0\).
This property ensures that opposites neutralize each other.
It's useful for balancing equations and understanding the nature of numbers.

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Most popular questions from this chapter

Given that \(0.3 \overline{3}=\frac{1}{3}\) and \(0.6 \overline{6}=\frac{2}{3},\) express each of the following as a ratio of two integers. $$0.9 \overline{9}$$

If \(n\) is positive and \(m\) is negative, what is the sign of \(n+(-m) ?\) Why?

List in order from least to greatest. $$13,-12,5,-17$$

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