fraction division

this method has been suggested by Caleb Gattegno, using an understanding that division is the inverse of multiplication and that the reciprocal is the multiplicative inverse (producing 1)

providing students with a few calculations of the form:

and encouraging them to cancel the result down will reveal a simple to see pattern
reasons for this can be fairly easily established








then, maybe following a simpler case (e.g. 2 x 3 x 4 = 24 with 2 x 3 = 24/4), it can be seen from:

that an equivalent statement can be formed