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