/*! 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 73 If \(n\) is a negative number, i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 73

If \(n\) is a negative number, is \(-n\) positive or negative?

Short Answer

Expert verified
\(-n\) is positive if \(n\) is negative.

Step by step solution

01

Understanding the Problem

We are given that \( n \) is a negative number and need to determine the sign of \( -n \). A negative number is any number less than zero. We will analyze what happens when we multiply the negative number by -1.
02

Apply the Concept of Multiplication by -1

Multiplying a negative number by -1 changes its sign. This is because the operation \( -n = (-1) imes n \) reflects the number across zero on the number line, moving it from a negative to a positive.
03

Determine the Sign of -n

Since multiplying \( n \) (which is negative) by -1 changes the sign, \(-n\) will be a positive number. This is because the sign of a number changes when it is multiplied by -1.

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.

Negative Numbers
Negative numbers are numbers less than zero. They lie to the left of zero on the number line. You can think of negative numbers as representing things like debt or a loss of points. Often denoted with a minus sign (e.g., -3), they are the opposite of positive numbers, which are greater than zero and lie to the right.
Working with negative numbers can sometimes be tricky, as they have properties that might be unfamiliar. For example:
  • Adding two negative numbers results in a more significant negative number.
  • Subtracting a negative number is like adding its positive counterpart.
Becoming comfortable with the behavior of negative numbers on the number line helps in visualizing their transformations.
Multiplication by -1
Multiplying by -1 is a special operation that reverses the sign of a number. It's like flipping the direction from which you view the number on the number line. For example, if you have -4 and multiply it by -1, you get 4. The negative sign moves from one side of zero to the other.
This function of changing signs is because:
  • Multiplying a positive number by -1 results in a negative number.
  • Multiplying a negative number by -1 results in a positive number.
So, when multiplying any number by -1, assess the number's original sign to determine the outcome.
Number Line
A number line is a visual representation that helps us understand numbers' positions and their relationships to each other. It is a straight line where numbers are placed at equal intervals, where 0 is typically in the center. On the number line:
  • Numbers to the right of zero are positive.
  • Numbers to the left of zero are negative.
Understanding the number line helps us visualize operations like addition, subtraction, and multiplication. For instance, when you multiply a number by -1, on the number line, it mirrors across zero, showing the change from one side (positive or negative) to the opposite side.

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

Simplify each of the following. $$2^{3}$$

Add or subtract. $$[3+10]+[8-2]$$

Work Problems \(55-60\) mentally, without pencil and paper or a calculator. The answer to the problem \(-52-49\) is closest to which of the following numbers? a. 100 b. 0 c\(-100\)

Write each of the following in symbols. The product of 7 and \(x .\)

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. $$8,3,-2, \dots$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

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.