Theory:

Zero \((0)\) is a rational number, and the sum of any rational number with zero\((0)\) results in the same rational number.
Thus, ab+0=0+ab=ab, for every rational number ab.
 
\(0\) is called the additive identity for rationals.
Example:
(i) Consider the rational number 35.
 
 Then, we have 35+0=0+35=35.
 
35+0=35+05=3+05=35 and similarly, 0+35=05+35=0+35=35.
 
Therefore, 35+0=0+35=35.
 
(ii) Consider the rational number 23.
 
Then, we have 23+0=0+23=23.
 
23+0=23+03=2+03=23 and similarly, 0+23=03+23=0+23=23.
 
Therefore, 23+0=0+23=23.
One \((1)\) is a rational number and the product of any rational number with one \((1)\) result in the same rational number.
For any rational number ab, we have ab×1=1×ab=ab.
 
\(1\) is called the multiplicative identity for rationals.
Example:
(i) Consider the rational number 34.
 
Then, we have 34×1=1×34=34.
 
34×1=34×14=3×14=34 and 1×34=14×34=1×34=34.
 
Therefore, 34×1=1×34=34.
 
(ii) Consider the rational 913.
 
Then, we have 913×1=1×913=913
 
913×1=913×113=9×113=913 and 1×913=113×913=1×913=913.
 
Therefore, 913×1=1×913=913.