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