/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 88 Give the opposite of each number... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 88

Give the opposite of each number. $$-5$$

Short Answer

Expert verified
The opposite of -5 is 5.

Step by step solution

01

Understanding Opposite Numbers

The opposite of a number is the number which, when added to the original number, equals zero. This means the opposite of a given number is simply its additive inverse. For a positive number like 5, the opposite would be -5, and vice versa.
02

Finding the Opposite of -5

Given the number, -5, we need to find its opposite. Since the opposite of a negative number is its positive version, the opposite of -5 is simply 5.
03

Verification

To verify, we can add -5 and its opposite, 5. \(-5 + 5 = 0\). Since the sum is zero, our calculation is confirmed correct.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding Additive Inverse
The concept of an additive inverse plays a vital role in mathematics. It's an operation that makes a number neutral or zero when added together. Consider a number, such as 3. The additive inverse of 3 is -3. When you add 3 and -3, the result is zero:
  • The formula is: \[x + (-x) = 0\]
This concept works in the same way for negative numbers. If you have -5, the additive inverse would be 5.

The beauty of the additive inverse is that it allows us to "cancel out" the value of the number with its opposite, leading us back to a neutral position, zero.
Exploring Number Line Concepts
A number line gives us a visual way to understand numbers and their opposites. Imagine a line with zero at the center, positive numbers to the right and negative numbers to the left.
  • If you start at zero and move right to +5, the opposite movement would be 5 steps to the left, which takes you to -5.
  • Likewise, if you begin at zero and shift left to -5, the opposite path would be 5 steps right, placing you at +5.
Number lines help visualize the idea that every number has an opposite, symmetrically located across the zero point.

This symmetry is key to understanding how additive inverses work in practice, making problems like finding the opposite of a number easier to grasp and solve.
Basic Arithmetic and Opposite Numbers
Basic arithmetic involves the fundamental operations of addition, subtraction, multiplication, and division. Opposite numbers primarily touch on the concept of addition and subtraction.

When you think of an opposite number, you're looking for one that, when added to your original number, equals zero. This is because opposite numbers effectively "cancel" each other out:
  • Example: When adding -4 and 4, the result is zero, as shown in the equation: \[-4 + 4 = 0\]
In subtraction, think of it as removing a value. If you subtract a negative, it's like adding a positive. This is where opposites are especially handy, as they simplify calculations and help achieve balance in equations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Subtract. $$-35-(-14)$$

In Chapter 1 we defined an arithmetic sequence as a sequence of numbers in which each number, after the first number, is obtained from the previous number by adding the same amount each time. Find the next two numbers in each arithmetic sequence below. $$8,3,-2, \dots$$

Rewrite the following using the associative property of multiplication. $$5(7 \cdot 8)=$$

Seattle, Washington, is 2 time zones west of New Orleans, Louisiana. Represent this time zone as a negative number, as discussed in the introduction to this chapter.

At 10: 00 in the morning in White Bear Lake, Minnesota, Zach notices the temperature is 5 degrees below zero Fahrenheit. Write this temperature as a negative number. By noon the temperature has dropped another 10 degrees. What is the temperature at noon?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.