Always. Rational numbers are closed under multiplication, because integers are: two rational numbers can be written as
[tex]\dfrac{a}{b},\quad \dfrac{c}{d}[/tex]
Their product is
[tex]\dfrac{a\cdot c}{b\cdot d}[/tex]
And both [tex]a\cdot c[/tex] and [tex]b\cdot d[/tex] are integers, because they are multiplications of integers.
So,
[tex]\dfrac{a\cdot c}{b\cdot d}[/tex]
is still a division between integers, and thus a rational.
