CLASS-7EXISTENCE OF MULTIPLICATIVE IDENTITY OF RATIONAL NUMBER

EXISTENCE OF MULTIPLICATIVE IDENTITY OF RATIONAL NUMBER -

The existence of the multiplicative identity property states that there is a unique number, called the multiplicative identity, which when multiplied by any rational number, leaves the number unchanged. For rational numbers, the multiplicative identity is 1.

Explanation:-

For any rational number a,

a × 1 = 1 × a = a

Examples: -

1) Rational Number as a Fraction:-

2

Let, a = ------

5

2               2          1          2

a X 1 = ------ X 1 = ------ X ------ = -------

5              5          1           5

2           1           2          2

1 X a = 1 X ------ = ------- X ------ = -------

5           1           5          5

So, a X 1 = 1 X a = a

2) Whole Number as a Rational Number:-

5

Let, a = 5              [Which can be written as -----]

1

5         1         5

a X 1 = ------ X ----- = ------ = 5

1         1         1

1         5         5

1 X a = ----- X ----- = ------ = 5

1         1         1

So, a X 1 = 1 X a = a

3) Negative Rational Number

- 3

Let,  a = ------

7

- 3          1       - 3

a X 1 = ------ X ----- = ------

7          1         7

1       - 3        - 3

1 X a = ----- X ------ = ------

1         7          7

So, a X 1 = 1 X a = a

In all these cases, multiplying by the multiplicative identity 1 leaves the rational number unchanged. This demonstrates the existence of the multiplicative identity property for rational numbers.