Question

The additive inverse of $\frac{-21}{-4}$ is

• A. $\frac{4}{21}$
• B. $\frac{-21}{4}$
• C. $\frac{-4}{21}$
• D. $\frac{21}{4}$

Answer 1

The correct option is B $\frac{-21}{4}$

For a rational number $\frac{a}{b}$, we have $\frac{a}{b}+(-\frac{a}{b})=(-\frac{a}{b})+\left(\frac{a}{b}\right)=0$.
We say that $(-\frac{a}{b})$ is the additive inverse of $\frac{a}{b}$ and $\frac{a}{b}$ is the additive inverse of $(-\frac{a}{b})$.

Here, we are asked to find the aditive inverse of $\frac{-21}{-4}$.
But $\frac{-21}{-4}=\frac{21}{4}$.
The additive inverse of $\frac{21}{4}$ is $-\frac{21}{4}$ as $\frac{21}{4}+(-\frac{21}{4})=(-\frac{21}{4})+\frac{21}{4}=0$