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Chapter 1: Problem 13

13\. \(-1+1\)

Short Answer

Expert verified
The result of \(-1 + 1\) is 0.

Step by step solution

01

Identify the Terms

The exercise is asking to evaluate the expression \(-1 + 1\). There are two terms in this expression: \(-1\) and \(+1\).
02

Apply Integer Addition Rules

Based on the rules for adding integers, when you add a negative number and a positive number with the same absolute value, they cancel each other out. Here, \(-1\) and \(+1\) are added together.
03

Compute the Result

Since the terms cancel each other, the sum of \(-1\) and \(+1\) is 0.

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Key Concepts

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

Absolute Value
The absolute value of a number is a way to describe how far the number is from zero on a number line, without considering its direction (positive or negative).
  • It is always a non-negative number.
  • For example, the absolute value of both \(-1\) and \(+1\) is 1.
We denote the absolute value of a number \(n\) by \(|n|\). So, \(|-1| = 1\) and \(|1| = 1\). The concept is crucial in integer addition, particularly when adding numbers with opposite signs. When the absolute values of these numbers are equal, they cancel each other out, resulting in zero.
Negative Numbers
Negative numbers are numbers less than zero, represented with a minus sign. These numbers are typically visualized as being to the left of zero on a number line.
  • In terms of real-world contexts, negative numbers can represent debts, lost temperatures, or any deficiency.
  • In mathematics, they are used to perform operations and express relationships.
For instance, in the expression \(-1 + 1\), the \(-1\) signifies that the value is one unit below zero on a number line. Understanding negative numbers and their properties will help in solving and simplifying expressions effectively.
Positive Numbers
Positive numbers are numbers greater than zero. They are the numeric values we most commonly encounter and are positioned to the right of zero on a number line.
  • These numbers do not have any sign before them unless it is explicitly shown as a plus sign \(+\).
  • For example, in the expression \(-1 + 1\), \(+1\) is a positive number.
In terms of integer addition, positive numbers can be added to other positive numbers to increase value, or they can counterbalance negative numbers. When \(-1\) is added to \(+1\), the positive and negative numbers balance each other out, leading to a sum of zero.

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Most popular questions from this chapter

27\. \(2 \sqrt{2}+\sqrt{31} 3 \sqrt{2}\)

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