Chapter 1: Q48. (page 16)

Identify the additive inverse and multiplicative inverse for each number
$- 4 \frac{3}{5}$

Short Answer

Expert verified

Additive inverse of $- 4 \frac{3}{5}$ is $4 \frac{3}{5}$ and multiplicative inverse of $- 4 \frac{3}{5}$ is $- \frac{5}{23}$

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 -435

Substitute $- 4 \frac{3}{5}$ for a

$a = - 4 \frac{3}{5}$

Multiply both sides by $- 1$

$\begin{matrix} (- 1) \times a = (- 1) \times (- 4 \frac{3}{5}) \\ - a = 4 \frac{3}{5} \end{matrix}$

Thus additive inverse of $- 4 \frac{3}{5}$ is $4 \frac{3}{5}$

- 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 -435

Substitute $- 4 \frac{3}{5}$ for a

$a = - 4 \frac{3}{5}$

Convert mix fraction into improper fraction

$\begin{matrix} a = - (4 + \frac{3}{5}) \\ a = - \frac{23}{5} \end{matrix}$

Take reciprocal on both sides

$\begin{matrix} \frac{1}{a} = \frac{1}{- \frac{23}{5}} \\ \frac{1}{a} = - \frac{5}{23} \end{matrix}$

Thus multiplicative inverse of $- 4 \frac{3}{5}$ is $- \frac{5}{23}$

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Identify the additive inverse and multiplicative inverse for each number
$- 4 \frac{3}{5}$

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of -435

- Define multiplicative inverse

- Multiplicative inverse of -435

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Identify the additive inverse and multiplicative inverse for each number-435

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of -435

- Define multiplicative inverse

- Multiplicative inverse of -435

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Geometry

Decision Maths

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Identify the additive inverse and multiplicative inverse for each number
$- 4 \frac{3}{5}$