Here I go again with these proofs, this time I am trying to prove the sum of two rational numbers is rational.

This is what I have...

Assume x is rational

Assume y is rational

Let x=a/b where a and b are integers and b does not equal 0

Let y=c/d where c and d are integers and d does not equal 0

x+y=a/b+c/d=(ad+bc)/bd

Let w=ad+bc

Let v=bd

We check that w and v are integers which they are and the integers are closed under addition and multiplication

Therefore the sum of two rational numbers is rational