How do you find the additive and multiplicative inverse of -5/8?

Question

13736 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-26T19:38:42

Additive inverse, $\frac{5}{8}$ $5/8$
Multiplicative inverse, $- \frac{8}{5}$ $-8/5$

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

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

Thus, for $a = - \frac{5}{8}$ $a = -5/8$
It's additive inverse be $c$ $c$ .

Then $- \frac{5}{8} + c = 0$ $-5/8 + c = 0$

Now, adding $\frac{5}{8}$ $5/8$ to both sides,

$c = \frac{5}{8}$ $c = 5/8$ .

Let the multiplicative inverse be $b$ $b$ .

Then $a \cdot b = 1$ $a*b = 1$
$\Rightarrow - \frac{5}{8} \cdot b = 1$ $implies -5/8*b = 1$

Multiplying both sides with $- \frac{8}{5}$ $-8/5$

$b = - \frac{8}{5}$ $b = -8/5$