Question

Find the product of additive inverse and multiplicative inverse of $-\frac{1}{3}$.

Answer 1

Step 1: State the given data and determine the additive inverse

The given fraction is $-\frac{1}{3}$.

As we know, the additive inverse of a number can be defined as the number with the opposite sign.

i.e., the additive inverse of a number $n$ is $-n$

So, the additive inverse of $-\frac{1}{3}$ is $-\left(-\frac{1}{3}\right)=\frac{1}{3}$ $\left[\because -\left(-a\right)=+a\right]$

Step 2: Determine the multiplicative inverse

Again, as we know the multiplicative inverse of a number can be defined as $1$ divided by the number.

i.e., the multiplicative inverse of a number $n$ is $\frac{1}{n}$.

So, the multiplicative inverse of $-\frac{1}{3}$ is $\frac{1}{\left(-{\displaystyle \frac{1}{3}}\right)}=-\frac{3}{1}=-3$ $\left[\because 1÷\frac{a}{b}=1\times \frac{b}{a}\right]$

Step 3: Calculate the required product

So, the required product can be calculated as,

The required product $=$ multiplicative inverse of $-\frac{1}{3}\times$ additive inverse of $-\frac{1}{3}$

$\Rightarrow$ Required product $=\frac{1}{3}\times \left(-3\right)$

$\Rightarrow$ Required product $=-\frac{1}{3}\times 3$

$\Rightarrow$Required product $=-1$

Hence, the product of additive inverse and multiplicative inverse of $-\frac{1}{3}$ is $-1$