/*! 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 61 (a) Identify the additive invers... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 61

(a) Identify the additive inverse and (b) Identify the multiplicative inverse, if possible. $$ -8 $$$$ -8 $$$$ -8 $$$$ -8 $$$$ -8 $$

Short Answer

Expert verified
Additive inverse: \(8\). Multiplicative inverse: \(-\frac{1}{8}\).

Step by step solution

01

Define Additive Inverse

The additive inverse of a number is a number that, when added to the original number, will sum to zero. For a given number \(a\), the additive inverse is \(-a\).
02

Find Additive Inverse of -8

Given the number \(-8\), its additive inverse is \(8\) because \(-8 + 8 = 0\).
03

Define Multiplicative Inverse

The multiplicative inverse (or reciprocal) of a number is a number that, when multiplied with the original number, will result in one. For a given number \(a\), the multiplicative inverse is \(\frac{1}{a}\).
04

Find Multiplicative Inverse of -8

Given the number \(-8\), its multiplicative inverse is \(-\frac{1}{8}\) because \(-8 \times -\frac{1}{8} = 1\).

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.

Additive Inverse
In algebra, the **additive inverse** of a number is what you add to a number to get zero. It's essentially the opposite of the given number. For example, for any number \( a \), the additive inverse is \( -a \).

So, when given the number \( -8 \), the additive inverse is \( 8 \) because:

- \( -8 + 8 = 0 \)

In simpler terms, the additive inverse of a number is just its negative (or positive) counterpart. This concept is crucial for solving algebraic equations because balancing equations often requires using additive inverses to isolate variables.
Multiplicative Inverse
The **multiplicative inverse**, also known as the reciprocal, is a number that, when multiplied by the original number, equals one. This is different from the additive inverse. In this case, for a number \( a \), the multiplicative inverse is \( \frac{1}{a} \).

For the given number \( -8 \), its multiplicative inverse is \( -\frac{1}{8} \) because:

- \( -8 \times -\frac{1}{8} = 1 \)

Multiplicative inverses are particularly useful in solving algebraic equations, especially when you need to divide by a number. Instead of dividing, you can multiply by the reciprocal!
Reciprocal
The **reciprocal** of a number is just another term for the multiplicative inverse. Reciprocals are used to flip a number over. For example, the reciprocal of a fraction \( \frac{a}{b} \) is \( \frac{b}{a} \).

For whole numbers, you can think of them as being over 1. So, the reciprocal of \( -8 \) is \( -\frac{1}{8} \) since \( -8 \) can be written as \( \frac{-8}{1} \). When flipped, it's \( -\frac{1}{8} \).

Reciprocals are quite powerful in algebra and are often used in division problems. Rather than dividing by a fraction, you multiply by its reciprocal. This is another tool that makes solving equations more manageable.

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

Explain the similarity in simplifying the given expressions. a. \((x+3)(x-3)\) b. \((\sqrt{x}+\sqrt{3})(\sqrt{x}-\sqrt{3})\)

Multiply and simplify. $$ (2 x-5)(x+4) $$

Simplify each expression. $$ (2 y-7)(2 y+7)-(2 y-7)^{2} $$

Determine if the statement is true or false. The product of two polynomials each of degree 4 will be degree 8 .

Multiply and simplify. $$ \left(-6 a^{5} b\right)\left(\frac{1}{3} a^{2} b^{2}\right) $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

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.