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Chapter 10: Problem 9

Find the opposite of each number. -6

Short Answer

Expert verified
The opposite of -6 is 6.

Step by step solution

01

Understand the Concept of Opposite Numbers

Opposite numbers, also called additive inverses, are pairs of numbers that sum up to zero. For a given number, its opposite is the number equidistant from zero on the number line but in the opposite direction.
02

Identify the Number

In this exercise, we are given the number -6.
03

Find the Opposite

To find the opposite, you switch the sign of the number. The opposite of -6 is 6, since -6 + 6 = 0.

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Key Concepts

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

Additive Inverses
Additive inverses, often referred to as opposite numbers, play a crucial role in mathematics. The main idea is that when you add a number to its additive inverse, the result is always zero. This is because they cancel each other out.

For example, consider the number \(-6\). Its additive inverse is \(6\) because \(-6 + 6 = 0\). This property is very useful in simplifying algebraic expressions and solving equations.
  • The additive inverse of a positive number is negative and vice versa.
  • Decimals, fractions, and whole numbers all have additive inverses.
  • The additive inverse of zero is zero itself, since \(0 + 0 = 0\).
The concept is simple but fundamental and serves as a building block for more advanced topics in mathematics.
Number Line
The number line is a visual representation of numbers in a straight line. Here, numbers are placed at equal intervals, and they extend infinitely in both the positive and negative directions. The number line provides a way to easily grasp the concept of opposite numbers.

Important features of the number line include:
  • Zero is at the central point, serving as a reference.
  • Positive numbers lie to the right of zero.
  • Negative numbers extend to the left of zero.
When locating the opposite of a number, find its position on the number line, then locate the same distance from zero in the opposite direction. For example, to find the opposite of \(-6\), look six units to the left of zero, then count six units to the right. This helps in quickly identifying and understanding additive inverses visually.
Integers
Integers are a set of numbers that include all positive whole numbers, negative whole numbers, and zero. These numbers do not have fractions or decimals.
  • Examples include \(-3, 0, 7\).
  • Integers can be categorized into positive integers (e.g., 1, 2, 3), negative integers (e.g., \(-1, -2, -3\)), and zero.
  • Every integer has an opposite, or additive inverse, within the integer set.
In the exercise of finding the opposite, we are essentially identifying the opposite integer. For \(-6\), the integer \(6\) acts as its additively inverse, balancing it out to zero. Working with integers is a foundational skill that appears in many areas of mathematics, especially in solving equations and inequalities.

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Most popular questions from this chapter

Find the value of \(-6-(-8)\).

Find each value. |-16|

For the following 18 problems, perform each subtraction. Use a calcula tor to cherk each result. $$ -5-(-3) $$

Convert \(3.2 \frac{3}{5}\) to a fraction.

Determine each of the values. $$ |-26| $$
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