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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

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