# CLASS-7INVERSE PROPERTY OF DIVISION OF RATIONAL NUMBER

INVERSE PROPERTY OF DIVISION OF RATIONAL NUMBER -

Every non-zero rational number has a multiplicative inverse (reciprocal). Dividing by a number is equivalent to multiplying by its reciprocal.

For a rational number -

a                                                       b

-------​ (where a ≠ 0, and b ≠ 0), its reciprocal is ------

b                                                       a

a           a

------- ÷ ------- = 1

b           b

This property allows us to rewrite division as multiplication by the reciprocal:-

a          c          a          c

------ ÷ ------ = ------ x ------

b          d          b          d

The inverse property of division for rational numbers is closely related to the concept of multiplicative inverses. For any non-zero rational number a, there exists another rational number 1/a (the multiplicative inverse of a) such that:

a ÷ a = 1

This can also be expressed in terms of multiplication as:-

1

a x ------- = 1

a

Here, 1/a​ is the multiplicative inverse of a, and dividing any non-zero rational number by itself results in 1.

3

Example.1) For a = ------

4

3           3

So, a ÷ a = ------- ÷ -------

4            4

3           4

Or, a x ------ = ------- x ------- = 1

a           4           3

13

Example.2) For a = ------

9

13         13

So, a ÷ a = ------ ÷ ------

9          9

1          13          9

Or, a x ------ = ------- x ------ = 1

a           9          13

33

Example.3) For a = (-) -------

21

33              33

So, a ÷ a = (-) ------- ÷ (-) -------

21              21

1              33              21

Or, a x ------ = (-) ------- x (-) ------- = 1

a              21              33