Will the difference of two rational numbers be always rational

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

1.) D

2.) A

3.) C

4.) C

5.) B

6.) A

7.) A

8.) Corresponding angles

9.) Vertical angles

10.) Transitive property

11.) Vertical angles

12.) Alternate interior

13.) P is parallel to R

14.) Given

15.) Given

16.) ∠5 and ∠2 equal 180°

17.) consecutive interior angles

18.) A is parallel to B