In the classroom: Pegboard multiplication of a fraction by a fraction

When a fraction is divided by a proper fraction, the answer is always larger than the dividend. In comparison, when a proper fraction is multiplied by a proper fraction, the answer is always smaller than either fraction involved. This is rather confusing to students who have observed that the product of two whole numbers is larger than either factor, except when one or both factors are 0 or 1. They have also observed that the answer when dividing whole numbers, excluding 1 as a divisor, is smaller than the dividend.