Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:
(i) 
(ii) 
(iii) 
(iv)
(i) Reaaranging and grouping the numbers in pairs in such a way that each group contains a pair of rational numbers with equal denominator
We have,
+ 
+ 
+ 
- 
+ 
- 
= 
+ 
= 
+ 
= 
= 
(ii) Reaaranging and grouping the numbers in pairs in such a way that each group contains a pair of rational numbers with equal denominator
We have,
+ 
+ 
+ 
- 
+ 
- 
= 
+ 
= 
+ 
= 
+ 
= 
(iii) Reaaranging and grouping the numbers in pairs in such a way that each group contains a pair of rational numbers with equal denominator
We have,
+ 
+ 
+ 
+ 
+
+ 
- 
- 
= 
+ 
- 
= 
+ 
+ 
= 
+ 
- 
= 
= 
(iv) Reaaranging and grouping the numbers in pairs in such a way that each group contains a pair of rational numbers with equal denominator
We have,
+ 0 + 
+ 
+ 
- 
+ 
+
+ 
= 
+ 
- 
= 
+ 
- 
= 
- 
= 
– 
= 
- 
= 