Chapter 1: Q46. (page 16)

Identify the additive inverse and multiplicative inverse for each number
$- \frac{5}{8}$

Short Answer

Expert verified

Additive inverse of $- \frac{5}{8}$ is $\frac{5}{8}$ and multiplicative inverse of $- \frac{5}{8}$ is $- \frac{8}{5}$

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 -58

Substitute $- \frac{5}{8}$ for $a$

$a = - \frac{5}{8}$

Multiply both sides by $- 1$

$\begin{matrix} (- 1) \times a = (- 1) \times (- \frac{5}{8}) \\ - a = \frac{5}{8} \end{matrix}$

Thus additive inverse of $- \frac{5}{8}$ is $\frac{5}{8}$

- 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 -58

Substitute $- \frac{5}{8}$ for a

$a = - \frac{5}{8}$

Take reciprocal on both sides

$\begin{matrix} \frac{1}{a} = \frac{1}{- \frac{5}{8}} \\ \frac{1}{a} = - \frac{8}{5} \end{matrix}$

Thus multiplicative inverse of $- \frac{5}{8}$ is $- \frac{8}{5}$

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Identify the additive inverse and multiplicative inverse for each number
$- \frac{5}{8}$

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of -58

- Define multiplicative inverse

- Multiplicative inverse of -58

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Identify the additive inverse and multiplicative inverse for each number-58

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of -58

- Define multiplicative inverse

- Multiplicative inverse of -58

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Decision Maths

Pure Maths

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Identify the additive inverse and multiplicative inverse for each number
$- \frac{5}{8}$