Multiplicative Properties of Rational Numbers -Inverse and Identity Property

There are two basic multiplicative properties of rational numbers.

(1) Multiplicative Identity Property

(2) Multiplicative Inverse Property

Let us understand these properties with examples.

(1) Multiplicative Identity Property: Multiplicative Identity Property of rational numbers states the product of for any rational number and 1 is the rational number itself.

Here, 1 is the multiplicative identity for rational numbers.

If (a/b) is any rational number, then

a/b x 1 = 1 x a/b

Example: 3/5 x 1 = 1 x 3/5

(2) Multiplicative Inverse Property: Multiplicative Inverse Property of rational numbers states that for every rational number a/b, b ≠ 0 there exists a rational number b/a such that

a/b x b/a =1

In this case a rational number b/a is multiplicative inverse of a rational number a/b.

Examples 3/5 x 5/3 = 1

The multiplicative inverse of 1/5 is 5.

Every rational number multiplied with 0 gives 0.

If a/b is any rational number then

a/b x 0 = 0 x a/b = 0

For example 2/3 x 0 = 0 x 2/3 = 0

Multiplicative inverse of 1/8 is 8.

1/8 x 8 = 1

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