Lattice Multiplication

Date: 8/30/96 at 10:3:13
From: by way of Eric Sasson
Subject: Lattice Multiplication

Can you please explain the lattice method of solving a multiplication
problem?

Thanks,
Susan

Date: 10/19/96 at 21:42:39
From: Doctor Mason
Subject: Re: Lattice Multiplication

Dear Susan,

You've asked one of my favorite questions.  In fact, your question is 
why I became a Math Doctor.

The Lattice Form of Multiplication dates back to the 1200s or 
before in Europe.  It gets its name from the fact that to do the 
multiplication you fill in a grid which resembles a lattice one 
might find ivy growing on.  Let me see if I can explain it with an 
example. Let's multiply 469 x 37.

First write the 469 across the top, and the 37 down the right side of 
a 3x2 rectangle.  (It's 3x2 because the factors have three and two 
digits respectively.)

      

Now fill in the lattice by multiplying the two digits found at 
the head of the column and to the right of the row. When the partial 
product is two digits, the first (10's) digit goes above the diagonal 
and the second (1's) digit goes on the lower right of the diagonal.  
If the partial product is only one digit, a zero is placed in the 
triangle above the diagonal in the square.

     

At this point, we have the multiplication done.  Now we add along the 
diagonals beginning in the lower right to get the final product.  Any 
"carries" when adding are illustrated outside the rectangle.

 

Multiplication really takes three steps:  multiply, carry, add.  
The method we typically use does the multiply and carry steps 
together. The lattice method does all three steps separately, so it's 
really easier!  Centuries ago, the Germans had a method for doing all 
three steps at once.  That method takes a lot of concentration!

Hope you enjoyed seeing this.  I really think it's fun.  
Let us know if you have any more questions!

-Doctor Mason,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/