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
1 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