Question

Write additive inverse and multiplicative inverse of $\frac{1}{5}$.

Answer 1

Find the additive inverse and multiplicative inverse of $\frac{1}{5}$.

When we add a number and its additive inverse, the sum is zero. To find the additive inverse of a number, we have to change the sign of the number.

The additive inverse of a number $a$ is $-a$.

$\Rightarrow a+\left(-a\right)=0$

So, additive inverse of $\frac{1}{5}$ is $-\frac{1}{5}$ as $\frac{1}{5}+(-\frac{1}{5})=0$

When we multiply a number and its multiplicative inverse, the product is one. To find the multiplicative inverse of a number, determine the reciprocal of the number.

The multiplicative inverse of a number $a$ is $\frac{1}{a}$.

$\Rightarrow a\times \frac{1}{a}=1$

So, multiplicative inverse of $\frac{1}{5}$ is $5$ as $\frac{1}{5}\times 5=1$

Therefore, the additive inverse and multiplicative inverse of $\frac{1}{5}$ is $-\frac{1}{5}$ and $5$ respectively.