Property of Rational Numbers – Additive Identity and Additive Inverse

There are two basic additive properties of rational numbers.

(1) Additive Identity Property

(2) Additive Inverse Property

(1) Additive Identity Property: Additive identity of rational numbers states that the sum of any rational number (a/b) and zero is the rational number itself. Suppose a/b is any rational number, then

a/b + 0 = 0 + a/b = a/b

Here 0 is called the additive identity of rational numbers.

We understand with example,

4/7 + 0 = 0 + 4/7 = 4/7

(2) Additive Inverse Property: The additive inverse property of rational numbers states that if a/b is a rational number, then there exists a rational number (-a/b) such that

a/b + (-a/b) = (-a/b) + a/b = 0

Here 0 is called the additive identity of rational numbers.

We understand with example,

2/3 + (-2/3) = (-2/3) + 2/3 = 0

Example: If a and b are rational numbers such that a + b = 0,

then a and b are additive inverse of each other.

For a rational number x/y additive inverse is (-x/y).