# CLASS-9PROPERTIES OF ADDITION ON RATIONAL NUMBERS

PROPERTIES OF ADDITION ON RATIONAL NUMBER

1) Commutative Law – Addition of rational numbers is commutative.

w          y              y          w

So, ( ------ + ------ ) = ( ------ + ------ )

x          z              z          x

2) Associative Law – Addition of rational numbers is associative

w          y           u          w            y          u

So, ( ------ + ------ ) + ------ = ------ + ( ------ + ------ )

x          z           v           x           z          v

3) Existence of Additive Identity0 is the additive identity on rational numbers

x                        x             x

( ------- + 0 ) = ( 0 + ------- ) = -------

y                        y             y

4) Existence of Additive Inverse –

x          - x

Every rational number ------ has ------ as its additive inverse

y            y

x        - x          - x           x

( ------ + ------ ) = ------- + ------- = 0

y          y            y            y

- x           x

and, the additive inverse of ------- is ------- as

y           y

- x          x            x         - x

( ------ + ------ ) = ------- + -------  =  0

y          y             y           y