Question

Is the difference of two rational a rational number? justify your answer with an example.

Answer 1

Yes , for example:)
-3-(-4)
-1 ans

Answer 2

Claim :- The difference between 2 rational number is always a rational number.

Proof :- You have a/ b - c/ d with a, b , c, d being integers and b, d not equal to 0 .

Then a/ b - c/ d ----> ad/ bd - bc/ bd --->

( ad- bc) / bd

Since ad , bc and bd are integers since integers are closed under the operation of the multiplication and ad- bc is an integer , since integers are closed under the operation of the subtraction , then( ad- bc ) / bd is a rational number since it is in the form of 1 integer divuded by another and the denominator is not equal to 0 , since b and d are not equal to 0

Thus a/ b - c/ d us a rational number