Verify associativity of addition of rational numbers i.e., when:
(i)
(ii)
(iii)
(iv)
(i) In order to verify this property, let us consider the following expressions:
Verification: + [ + (-)] = + [ - ]
= +
=
=
And,
( + ) + () = ( + ) -
= -
=
=
Therefore,
The associative property of additional of rational numbers has been verified
(ii) In order to verify this property, let us consider the following expressions:
Verification: + [ + (-)] = + [ - ]
= +
=
=
And,
( + ) + () = ( + ) -
= -
=
=
Therefore,
The associative property of additional of rational numbers has been verified
(iii) In order to verify this property, let us consider the following expressions:
Verification: + [ + (-)] = + [ - ]
= -
=
=
And,
(- + ) + () = ( -) -
= -
=
=
Therefore,
The associative property of additional of rational numbers has been verified
(iv) In order to verify this property, let us consider the following expressions:
Verification: -2 + [ + (-)] = -2 + [ - ]
= -2 -
=
=
And,
(-2 +) + () = ( + ) -
= -
=
=
Therefore,
The associative property of additional of rational numbers has been verified