# What is the opposite and reciprocal of 1/3?

Jun 25, 2015

-3.

#### Explanation:

To find the opposite/reciprocal of a number, flip it and add a negative (or take it away if the number is negative already).

$\frac{1}{3} \to \frac{3}{1}$

$\frac{3}{1} \to - \frac{3}{1}$

Jun 25, 2015

The opposite of $\frac{1}{3}$ is $- \frac{1}{3}$,
and the reciprocal of $\frac{1}{3}$ is $3$.
The opposite (also known as the additive inverse) is the number we have to add to get an answer equal to the additive identity, $0$. Since $\frac{1}{3} + \left(- \frac{1}{3}\right) = \left(- \frac{1}{3}\right) + \frac{1}{3} = 0$, the opposite of $\frac{1}{3}$ is $- \frac{1}{3}$.
The reciprocal (also known as the multiplicative inverse) is the number we have to multiply to get an answer equal to the multiplicative identity, $1$. Since $\frac{1}{3} \times 3 = 3 \times \frac{1}{3} = 1$, the reciprocal of $\frac{1}{3}$ is $3$.
(It may help to remind you that $3 = \frac{3}{1}$.)