Question

How do you find the additive and multiplicative inverse of $\left(-\frac{8}{3}\right)$?

Answer 1

Step 1: Define the multiplicative and additive inverse

1. Additive inverse of a number can be defined as the number with the opposite sign.
2. For example, the additive inverse of a number $n$ is $-n$.
3. Multiplicative inverse of a number can be defined as $1$ divided by the number.
4. For example, the multiplicative inverse of a number $n$ is $\frac{1}{n}$.

Step 2: Find the multiplicative and additive inverse of the given number

The given fraction is $\left(-\frac{8}{3}\right)$.

The additive inverse of $\left(-\frac{8}{3}\right)$ is $-\left(-\frac{8}{3}\right)=\frac{8}{3}$ $\left[\because -\left(-a\right)=+a\right]$

And, the multiplicative inverse of $\left(-\frac{8}{3}\right)$ is $\frac{1}{\left(-{\displaystyle \raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}=-\frac{1}{{\displaystyle \raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}=-\frac{3}{8}$ $\left[\because 1÷\frac{a}{b}=1\times \frac{b}{a}\right]$

Hence, the additive inverse and multiplicative inverse of $\left(-\frac{8}{3}\right)$ are $\frac{8}{3}$ and $-\frac{3}{8}$ respectively.