Chapter 1: Q43. (page 16)

Identify the additive inverse and multiplicative inverse for each number
$- 10$

Short Answer

Expert verified

Additive inverse of $- 10$ is 10 and multiplicative inverse of $- 10$ is $- \frac{1}{10}$

Step by step solution

- Define additive inverse

Let ‘a’ be a real number such that

$a + (- a) = 0 = (- a) + a$

Then ‘ $- a$ ’ is the additive inverse of ‘a’

- Additive inverse of -10

Substitute $- 10$ for a

$a = - 10$

Multiply both sides by $- 1$

$\begin{matrix} (- 1) \times a = (- 1) \times (- 10) \\ - a = 10 \end{matrix}$

Thus additive inverse of $- 10$ is 10

- Define multiplicative inverse

Let ‘a’ be a real number with $a = 0$ such that

$a \cdot \frac{1}{a} = 1 = \frac{1}{a} \cdot a$

Then ‘ $\frac{1}{a}$ ’ is the multiplicative inverse of ‘a’

- Multiplicative inverse of -10

Substitute $- 10$ for a

$a = - 10$

Reciprocal on both sides

$\begin{matrix} \frac{1}{a} = \frac{1}{- 10} \\ \frac{1}{a} = - \frac{1}{10} \end{matrix}$

Thus multiplicative inverse of $- 10$ is $- \frac{1}{10}$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Identify the additive inverse and multiplicative inverse for each number
$- 10$

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of -10

- Define multiplicative inverse

- Multiplicative inverse of -10

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Probability and Statistics

Calculus

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Identify the additive inverse and multiplicative inverse for each number-10

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of -10

- Define multiplicative inverse

- Multiplicative inverse of -10

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Probability and Statistics

Calculus

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Identify the additive inverse and multiplicative inverse for each number
$- 10$