If you multiply two rational numbers, you get another rational number.
In fact, rational numbers are defined as the ratio between two integers, as long as the denominator is not zero.
Moreover, the product between rational works like this:
[tex]\dfrac{a}{b}\cdot\dfrac{c}{d} = \dfrac{ac}{bd}[/tex]
Now, all the numbers a,b,c and d are integers, which means that ac is the product of two integers, and so is bd.
The product of two integers is still an integer, and thus ac/bd is still a ratio between integers, and thus the product between rationals is still a rational.
