How do you find the additive and multiplicative inverse of -10?

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Answer 1 · 2017-03-26T19:40:36

Additive inverse, $+ 10$ $+10$
Multiplicative inverse, $- \frac{1}{10}$ $-1/10$

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 $a = - 10$ $a = -10$
It's additive inverse be $c$ $c$ .

Then $- 10 + c = 0$ $-10 + c = 0$

Now, adding $10$ $10$ to both sides,

$c = 10$ $c = 10$ .

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

Then $a \cdot b = 1$ $a*b = 1$
$\Rightarrow - 10 \cdot b = 1$ $implies -10*b = 1$

Multiplying both sides with $- \frac{1}{10}$ $-1/10$

$b = - \frac{1}{10}$ $b = -1/10$