Existence of inverse:

**Additive inverse:**

3+ (-3)=0 and -3+3=0

-5+5=0 and 5+(-5)=____

2/3 + ?=0 and ____ + 2/3 = ___?

(-1/2)+?=0 and ? + (1/2)=____

Here -3 and 3 are called the additive inverses of each other because on adding them we get the sum ‘0’. Any two numbers whose sum is ‘0’ are called the additive inverse of each other.In general if a represents any rational number them a+(-a)=0 and (-a)+a= 0.

Then ‘a’, ‘-a’ are additive inverse of each other.

The additive inverse of 0 is only 0 as 0+0=0.

**Multiplicative inverse:**

By which rational number 2/7 is multiplied to get the produce 1?

We can see 2/7 * 7/2 = 1 and 7/2 * 2/7 = 1.

Any two numbers whose product is ‘1’ are called the multiplicative inverse of each other.

For example, 4 * 1/4 =1 and 1/4 * 4 =1 therefore the numbers 4 and 1/4 are the multiplicative inverse(or the reciprocals) of each other.

We say that rational number c/d is called the reciprocal are the multiplicative inverse of another rational number a/b if a/b *c/d=1