How do you find the additive and multiplicative inverse of 1/3?

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Answer 1 · 2017-03-26T19:33:45

Additive inverse, $- \frac{1}{3}$ $-1/3$
Multiplicative inverse, $3$ $3$

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 $a = \frac{1}{3}$ $a = 1/3$
It's additive inverse be $c$ $c$ .

Then $\frac{1}{3} + c = 0$ $1/3 + c = 0$

Now, adding $- \frac{1}{3}$ $-1/3$ to both sides,

$c = - \frac{1}{3}$ $c = -1/3$ .

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

Then $a \cdot b = 1$ $a*b = 1$
$\Rightarrow \frac{1}{3} \cdot b = 1$ $implies 1/3*b = 1$

Multiplying both sides with $3$ $3$

$b = 3$ $b = 3$