# How do you find the additive and multiplicative inverse of -8/3?

Apr 15, 2018

The additive inverse is $\frac{8}{3}$.
The multiplicative inverse is $- \frac{3}{8}$.

#### Explanation:

When a number is added to its additive inverse, the result zero. When a number is multiplied to its multiplicative inverse, the result is 1.

$- \frac{8}{3} + x = 0$
(add $\frac{8}{3}$ to both sides):
$x = \frac{8}{3}$
$- \frac{8}{3} \cdot x = 1$
(divide both sides by $- \frac{8}{3}$):
$x = - \frac{3}{8}$