ok, Im not totally sure about this.

but...

a rational number is a integer number or a fraction of two integers.

an irrational number is a number that can not be written as a fraction. (pi, sqrt(2), e for example)

therefore, when you multiply an irrational number with a rational number it has to be irrational (if the rational number isn´t zero)

for example multiplie pi with 1/4 the result is pi/4 but since you can´t write pi as a fraction you can´t write pi/4 as a fraction.