Question

What is the additive and multiplicative inverse of 2/3

Answer 1

The additive inverse of a number is the number that when added to the original number yields zero. This number is also known as the opposite (number) which involves sign change

Given that the original number is

`=(2)/(3)`

Let the additive inverse of the number above be

`=x`

Therefore,we will have

`\begin{gathered} x+(2)/(3)=0 \\ (3x+2)/(3)=0 \\ \text{cross multiply} \\ 3x+2=0*3 \\ 3x+2=0 \\ 3x=0-2 \\ 3x=-2 \\ (3x)/(3)=-(2)/(3) \\ x=-(2)/(3) \end{gathered}`

Hence,

The additive inverse = -2/3

A multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a

Let the multiplicative inverse be

`=y`

Hence,

we will have that

`\begin{gathered} y*(2)/(3)=1 \\ (2y)/(3)=1 \\ 2y=3 \\ (2y)/(2)=(3)/(2) \\ y=(3)/(2) \end{gathered}`

Hence,

The multiplicative inverse = 3/2