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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