Properties of Rational Numbers - Identity of Addition and Multiplication of Rational Numbers

Identity of Addition and Multiplication of rational number:

1. The Role of 0:

2 + 0 = 0 + 2 = 2.
You will find that when you add 0 to a whole number, the sum is again that whole number. This happens for integers and rational numbers also.

In general,
a + 0 = 0 + a = a, where a is a whole number
b + 0 = 0 + b = b, where b is an integer number
c + 0 = 0 + c = c, where c is a rational number

Zero is called the identity for the addition of rational numbers. It is the additive identity for integers and whole numbers as well.

2. The role of 1:

`-2/7 xx 1 = 1 xx -2/7 = -2/7`.

When you multiply any rational number with 1, you get back the same rational number as the product.

You will find that a × 1 = 1 × a = a for any rational number a.

We say that 1 is the multiplicative identity for rational numbers.