The lattice is a method of multiplication used in the Elizabethan era, and is a very good method of multiplication to this day. Below is what a basic lattice looks like:
This will handle the multiplication of two numbers both up to 9,999, although larger numbers can be accomodated through a larger lattice. Allow me to show you how it works.
We will be multiplying 2 4-digit numbers: 9,876 and 5,432.
First number:
Second number:
Row by row, multiply each digit of the first number by that row's digit of the second number. Write the result under the diagonal line running across each box in that row.
Note that 30 is a two-digit number. With two-digit numbers, write the "tens" digit in the upper part of the box, like this:
This is very important, so remember it.
Do this type of multiplication for every row in the lattice.
And here's what the result looks like:
Starting from the lower right-hand corner, add the numbers grouped together between the diagonal lines.
Here we have a problem! The result is 13, which has two digits. What we do here is write the second digit into the group of numbers between the next pair of diagonal lines, as shown below:
And the problem is fixed. If there is an empty space in the group, the number is usually written there, here, it's crammed into a space already occupied (which is fine.) Onto the next one:
We have run out of space along the bottom, which means we have to continue up the left side.