# CLASS-9PROPERTIES OF MULTIPLICATION ON RATIONAL NUMBERS

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