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

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Answer 1 · 2017-03-26T19:42:19

Additive inverse, $+ 8$ $+8$
Multiplicative inverse, $- \frac{1}{8}$ $-1/8$

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 $a = - 8$ $a = -8$
It's additive inverse be $c$ $c$ .

Then $- 8 + c = 0$ $-8 + c = 0$

Now, adding $8$ $8$ to both sides,

$c = 8$ $c = 8$ .

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

Then $a \cdot b = 1$ $a*b = 1$
$\Rightarrow - 8 \cdot b = 1$ $implies -8*b = 1$

Multiplying both sides with $- \frac{1}{8}$ $-1/8$

$b = - \frac{1}{8}$ $b = -1/8$