Question

Identify the additive inverse and multiplicative inverse for each number

10. $-8$

Short answer

Additive inverse of $-8$ is 8 and multiplicative inverse of $-8$ is $-\frac{1}{8}$

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 -8

Substitute $-8$for $a$

$a=-8$

Multiply both sides by -1

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

Thus additive inverse of $-8$is 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 -8

Substitute $-8$for a

$a=-8$

Reciprocal on both sides

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

Thus multiplicative inverse of $-8$ is $-\frac{1}{8}$ .