We can, however, show you why the algorithm works:
As you can see, we first wrote the division problem as a fraction with fractions for both its numerator and its denominator. Next, to change the messy denominator to a nice, tidy denominator, we multiplied by 1 in the form of (4/3)/(4/3). We then showed the multiplication problem as multiplying numerators and multiplying denominators. We computed the denominator, which was 1, and then divided by 1, which didn't change the numerator. We are left with 2/3 4/3, exactly as the algorithm tells us: The division problem 2/3 3/4 can be changed to the multiplication problem 2/3 4/3, and both will produce the same answer (8/9).
<< back to Part A: Models for the Multiplication and Division of Fractions