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Chapter 3: Problem 366

In the following exercises, find the opposite of each number. $$ -2 $$

Short Answer

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Step by step solution

01

Understanding Opposites

The opposite of a number is the number that, when added to the original number, equals zero. This is often referred to as the additive inverse.
02

Identify the Given Number

The given number is -2. We need to find its opposite.
03

Find the Opposite

The opposite of -2 is the number that, when added to -2, results in 0. To find this, we change the sign of -2.
04

Compute the Opposite

Changing the sign of -2 gives us 2, because -2 + 2 = 0.

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Key Concepts

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

Additive Inverse
The concept of the additive inverse is fundamental in prealgebra. Understanding this idea helps simplify multiple math problems. The additive inverse of a number is another number that, when added to the original number, results in zero. This means if you have a number 'a', its additive inverse is '-a'.

For example:
  • The additive inverse of 5 is -5, since 5 + (-5) = 0.
  • The additive inverse of -3 is 3, because -3 + 3 = 0.
Knowing how to find an additive inverse will help you understand how numbers relate to each other on the number line.

This concept is particularly handy when solving equations and balancing both sides. Almost any time you need to 'cancel out' a number, you'll use its additive inverse.
Opposite Numbers
Opposite numbers may sound confusing, but they are simply pairs of numbers that are the same distance from zero on the number line but in opposite directions. Another term commonly used for opposite numbers is 'negatives'.

For example:
  • 3 and -3 are opposite numbers. They are both 3 units away from zero, but on opposite sides.
  • -7 and 7 are also opposite numbers for the same reason.
Identifying opposite numbers is essential since it aligns with the idea of symmetry in mathematics. When added together, opposite numbers always equal zero.

This means, if you encounter a problem asking for the opposite of a number, you just need to change its sign. If it鈥檚 positive, make it negative. If it鈥檚 negative, make it positive. So, the opposite of -2 is 2, and the opposite of 4 is -4.
Integers
Integers are a broad category that includes whole numbers and their opposites. These numbers can be positive, negative, or zero. Unlike fractions or decimals, integers are whole units.

Examples of integers are:
  • -3
  • 0
  • 7
  • -10
Working with integers means you'll deal with their properties: adding, subtracting, and finding opposites. Integers are often shown on a number line, with zero in the middle, positive numbers to the right, and negative numbers to the left. This visual aid makes it easier to understand their relationships.

Understanding integers is crucial for many areas of math, including algebra, data analysis, and more advanced topics.

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Most popular questions from this chapter

In the following exercises, evaluate each expression. $$ 2 n^{2}-n+5 \text { when } n=-4 $$

In the following exercises, translate and solve. The product of \(-6\) and \(y\) is \(-42\)

In the following exercises, translate to an algebraic expression and simplify if possible. the product of \(-12\) and 6

In the following exercises, evaluate each expression. $$ \begin{array}{l}{n+4 \text { when }} \\ {\text { (a) } n=-1} \\ {\text { (b) } n=-20}\end{array} $$

In the following exercises, translate and solve. The product of \(-21\) and \(n\) is 63
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