Somebody that does not mind with more if a is a rational number and b is a rational number, then the product ab must be a) rational. b) imaginary. c) an integer. d) irrational.

The answer would be A)rational. 

The rational number is number that can be represented as a ratio of "a/b" where a and b is an integer. When you multiply two rational number of a/b and c/d, the result would be: a/b * c/d= ac/ bd
Since a and c is an integer, the product of ac would be integer too. The same thing applies to bd.
Since ac and bd is an integer, then ac/bd would be a rational number