# Find the product of additive inverse and multiplicative inverse of -1/3.

An additive inverse of a number is known as the value, resulting in a zero value when added to the original number. In order to yield zero, it is the value we add to a number. Assume, ‘a’ is the original number, then its additive inverse will be the minus of such that

a + (-a)

a – a

= 0

Given value is $$\frac{-1}{3}$$

Let us assume additive inverse as x

$$\frac{-1}{3}$$ + x = 0

x = $$\frac{1}{3}$$

The additive inverse of $$\frac{-1}{3}$$ is $$\frac{1}{3}$$.

## Multiplicative inverse

The multiplicative inverse also known as reciprocal implies is something which is opposite. The reciprocal number obtained in such a way that the value is equal to identity 1 when multiplied by the original number. Let us consider the number ‘a’ then the multiplicative inverse of the number is ‘1/a’.

a × 1/a = 1

Given value is $$\frac{-1}{3}$$ , so

$$\frac{-1}{3}$$× 1/$$\frac{3}{-1}$$

⇒ 1

The multiplicative inverse of $$\frac{-1}{3}$$ is $$\frac{3}{-1}$$= -3

### Product of additive inverse and multiplicative inverse

Sum of additive inverse and multiplicative inverse of

$$\frac{1}{3}$$ X -3

=-1

Product of additive inverse and multiplicative inverse of $$\frac{-1}{3}$$ -1