Question

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.

Answer 1

The best way to answer this is to find counterarguments for each answer to eliminate them as a possibility. ab doesn't have to be an integer, 2.5*3=7.5 . That's also not an imaginary number so that's out. And that's also not an irrational number so that's out too. Only choice left is rational number.

Answer 2

By definition, a rational number can be expressed as a fraction with integer values in the numerator and denominator (denominator not zero). So, multiplying two rationals is the same as multiplying two such fractions, which will result in another fraction of this same form since integers are closed under multiplication. Thus, multiplying two rational numbers produces another rational number.

So in this case your answer would be A.

Hope I helped!!!