Properties Of Multiplication On Rational Number –
1) Commutative Law :- Multiplication on rational numbers is commutative,
u w w u
( ------ X ------ ) = ( ------ X ------ )
v x x v
2) Associative Law :- Multiplication on rational numbers is associative,
u w y u w y
( ------ X ------ ) X ------ = ------- X ( ------- X ------ )
v x z v x z
3) Existence of Multiplicative Identity :- Clearly, 1 is the multiplicative identity in rational numbers.
x x x
As, 1 X -------- = -------- X 1 = --------
y y y
4) Existence of Multiplicative Inverse – for each non-zero rational x/y, there exists rational y/x such that
x y y x
-------- X -------- = -------- X -------- = 1
y x x y
x y
we can say that, the multiplicative inverse of ------ is -------
y x
x ˉ1 y
and we write, (----- ) = ------
y x