Question

Identify the additive inverse and multiplicative inverse for each number

$-\frac{5}{8}$

Short answer

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

$a+\left(-a\right)=0=\left(-a\right)+a$

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 $-1$

$\begin{array}{c}\left(-1\right)\times a=\left(-1\right)\times \left(-\frac{5}{8}\right)\\ -a=\frac{5}{8}\end{array}$

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

- Define multiplicative inverse

Let ‘a’ be a real number with $a\cancel{=}0$such that

$a·\frac{1}{a}=1=\frac{1}{a}·a$

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

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

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