WEEKLY WHINE

But who’s multiplying: Lattice multiplication

Long multiplication is a process, and mistakes in carrying are frequent. What if there was a way to do long multiplication that is just as long, but combines all the carrying into a single step? Well, there is, and it’s called lattice multiplication, or Gelosia multiplication, as introduced by Hindu mathematicians.

A grid is formed with the digits of the multiplicands along the top and right. Each pair of digits is multiplied; the tens digit of the result is placed above the diagonal, the units digit below. The resulting digits are summed along the diagonals, carrying as needed.

Like long multiplication, the problem is broken down into multiple steps. But this formulation uses simpler steps than does long multiplication, with correspondingly less chance of error. The need to write down each intermediate product means that lattice multiplication is also difficult to do mentally.

On the whole, though, this is clearly an easier approach to start with than long multiplication. So why would anyone continue to teach long multiplication, particularly when lattice multiplication has been available for such a long time? There does not seem to be a satisfactory answer.