Question

What is the opposite and reciprocal of $\frac{1}{3}$?

Answer 1

Step 1. Determine the opposite of $\frac{1}{3}$.

The term opposite represents the additive inverse of a number. The sum of the number and its additive inverse is 0.

The number which gives 0 on adding with $\frac{1}{3}$ is the negative of $\frac{1}{3}$, that is the number $-\frac{1}{3}$.

Therefore, the opposite of $\frac{1}{3}$ is $-\frac{1}{3}$.

Step 2. Determine the reciprocal of $\frac{1}{3}$.

The term reciprocal represents the multiplicative inverse of a number. The sum of the number and its multiplicative inverse is 1.

The number that gives 1 on multiplication with $\frac{1}{3}$ is 1 divided by $\frac{1}{3}$. Find the value of 1 divided by $\frac{1}{3}$:

$\begin{array}{rcl}\frac{1}{{\displaystyle \frac{1}{3}}}& =& 1\times \frac{3}{1}\\ & \Rightarrow & \frac{1}{{\displaystyle \frac{1}{3}}}=3\end{array}$

Therefore, the reciprocal of the number $\frac{1}{3}$ is $3$.