## Additive inverse

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

**Answer**

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