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That's only true if the fractions are "proper" fractions ... with numerator smaller than denominator. The reason is: If you take (a piece less than the whole thing) out of (a piece less than the whole thing), you wind up with a piece smaller than either of the original pieces.
A fraction is smaller than one if the number on the top is less than the number on the bottom.
if 1/2 x 1/3 then times it and get 1/6
if you mean multiplying something by a fraction where the numerator is smaller than the denominator then yes.
You don't