There are many counter examples to this. People seem to think multiplying two fractions will get you a whole number but it definitely isn't the case. Just take 1/2 and 2/3 as an example:
1/2 ÷ 2/3 (dividing is the same as multiplying by the reciprocal)
1/2 * 3/2 is 3/4 and that is not a whole number. Hope this helped.