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 Identity – 0 is the additive identity on rational numbers
x x x
( ------- + 0 ) = ( 0 + ------- ) = -------
y y y
4) Existence of Additive Inverse –
x - xEvery 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