# What is the opposite and reciprocal of -11/9?

May 25, 2018

The opposite and reciprocal of $- \frac{11}{9}$ is $\frac{9}{11}$.

#### Explanation:

The opposite of $- \frac{11}{9}$ is its additive inverse $\frac{11}{9}$. The sum of a number and its additive inverse equal $0$.

$\textcolor{red}{a} + \textcolor{b l u e}{- a} = \textcolor{p u r p \le}{0} = \textcolor{b l u e}{- a} + \textcolor{red}{a}$
The reciprocal of a fraction is its multiplicative inverse. The product of a number and its multiplicative inverse equals $1$.
$\textcolor{m a \ge n t a}{a} \times \textcolor{t e a l}{\frac{1}{a}} = \textcolor{p u r p \le}{1} = \textcolor{t e a l}{\frac{1}{a}} \times \textcolor{m a \ge n t a}{a}$
The multiplicative inverse of $\frac{11}{9}$ is $\frac{9}{11}$.