Problem 30 Identify the additive inverse an... [FREE SOLUTION]

Chapter 1: Problem 30

Identify the additive inverse and multiplicative inverse for each number. $$ -0.125 $$

Short Answer

Expert verified

The additive inverse of $-0.125$ is $0.125$ and the multiplicative inverse is $-8$.

Step by step solution

Define Additive Inverse

The additive inverse of a number is a number that, when added to the original number, results in zero. For any real number $x$, the additive inverse is $-x$.

Find the Additive Inverse of $-0.125$

To find the additive inverse of $-0.125$, we need to find a number that when added to $-0.125$ gives zero. Mathematically, this number is $0.125$ because: $-0.125 + 0.125 = 0$.

Define Multiplicative Inverse

The multiplicative inverse (or reciprocal) of a number is a number that, when multiplied by the original number, results in one. For any non-zero real number $x$, the multiplicative inverse is $\frac{1}{x}$.

Find the Multiplicative Inverse of $-0.125$

To find the multiplicative inverse of $-0.125$, we calculate $\frac{1}{-0.125}$. Therefore, \[\frac{1}{-0.125} = -8\]. This is because: $-0.125 \times -8 = 1$.

Summary of Inverses

The additive inverse of $-0.125$ is $0.125$ and the multiplicative inverse is $-8$.

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

The additive inverse is a simple yet crucial concept in mathematics. For any real number, the additive inverse is the value that brings the original number to zero when summed together.

The additive inverse of a real number $x$ is $-x$.
It always satisfies the equation: $x + (-x) = 0$.

In our given problem, we have the number -0.125.To find its additive inverse, we look for a number that, when added to -0.125, results in zero.
The answer is straightforward: it's 0.125.This is because $-0.125 + 0.125 = 0$. As you can see, the concept of an additive inverse helps us understand how numbers can form perfect balances with their opposites.

Multiplicative Inverse

A multiplicative inverse is also known as a reciprocal. This is the number that multiplies with a given number to yield one.

For any non-zero real number $x$, the multiplicative inverse is $\frac{1}{x}$.
This satisfies the equation: $x \times \frac{1}{x} = 1$.

Multiplicative inverses are crucial when solving equations or simplifying expressions. For number -0.125, the goal is to find its reciprocal.
To do this, simply set up the division: $-0.125$, which equals $\frac{1}{-0.125}$.
On solving it through calculation, we find this equals to $-8$.
This means when $-0.125$ is multiplied by $-8$, it results in 1, which confirms that -8 is indeed the multiplicative inverse.

Real Numbers

Real numbers are an essential part of mathematics, covering every number imaginable from the negative to positive infinity, including everything in between: integers, rational numbers, and irrational numbers.
These numbers can be represented on a number line, which helps visualize concepts like inverses. The concept of real numbers is significant when discussing additive and multiplicative inverses.

For real numbers, the additive inverse always exists and is simply a number's negative counterpart.
The multiplicative inverse is present for all non-zero real numbers and provides a foundation for many algebraic processes.

Real numbers allow mathematicians to explore and understand the properties of numbers within a continuous framework, making them an indispensable part of arithmetic and higher-level math.

One App. One Place for Learning.

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

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Identify the additive inverse and multiplicative inverse for each number. $$ -0.125 $$

Short Answer

Step by step solution

Define Additive Inverse

Find the Additive Inverse of \(-0.125\)

Define Multiplicative Inverse

Find the Multiplicative Inverse of \(-0.125\)

Summary of Inverses

Key Concepts

Additive Inverse

Multiplicative Inverse

Real Numbers

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.