Verify commutativity of addition of rational numbers for each of the following pairson of rational numbers:

(i) and

(ii) and

(iii) and

(iv) and

(v) 4 and

(vi) -4and

(i) The addition of rational number is commutative

i.e, if and are any two rational numbers, then

+ = +

Verification: In order to verify this property,

Let us consider two expressions:

+

And,

+

We have:

+ = +

=

=

And,

+ = +

=

=

Therefore,

+ = +

(ii) The addition of rational number is commutative

i.e, if and are any two rational numbers, then

+ = +

Verification: In order to verify this property,

Let us consider two expressions:

+

And,

+

We have:

+ = +

=

=

And,

+ = +

=

=

Therefore,

+ = +

(iii) The addition of rational number is commutative

i.e, if and are any two rational numbers, then

+ = +

Verification: In order to verify this property,

Let us consider two expressions:

+

And,

+

We have:

+ = +

=

=

And,

+ = +

=

=

Therefore,

+ = +

(iv) The addition of rational number is commutative

i.e, if and are any two rational numbers, then

+ = +

Verification: In order to verify this property,

Let us consider two expressions:

+

And,

+

We have:

+ = +

=

=

And,

+ = +

=

=

Therefore,

+ = +

(v) The addition of rational number is commutative

i.e, if and are any two rational numbers, then

+ = +

Verification: In order to verify this property,

Let us consider two expressions:

4 +

And,

+ 4

We have:

4 + = -

=

=

And,

+ 4 = +

=

=

Therefore,

4 + = + 4

(vi) The addition of rational number is commutative

i.e, if and are any two rational numbers, then

+ = +

Verification: In order to verify this property,

Let us consider two expressions:

+

And,

- 4

We have:

-4 + = -

=

=

And,

- 4 = -

=

=

Therefore,

-4 + = -4

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