Question

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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 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