# How do you find the additive and multiplicative inverse of 1.5?

Mar 26, 2017

Additive inverse, $- 1.5$
Multiplicative inverse, $\frac{2}{3}$ or $0.67$

#### Explanation:

For a number $a$, it's multiplicative inverse $b$ is such that $a \cdot b = 1$ which is the multiplicative identity.

For a number $a$, it's additive inverse $c$ would be such that $a + c = 0$ where $0$ is additive identity.

Thus, for $a = 1.5 = \frac{3}{2}$
It's additive inverse be $c$.

Then $\frac{3}{2} + c = 0$

Now, adding $- \frac{3}{2}$ to both sides,

$c = - \frac{3}{2} = - 1.5$

Let the multiplicative inverse be $b$.

Then $a \cdot b = 1$
$\implies \frac{3}{2} \cdot b = 1$

Multiplying both sides with $\frac{2}{3}$

$b = \frac{2}{3} = 0.67$