Lattice multiplication

Type a multiplication with × or x between the numbers, like 47 × 36 or 3.2 x 1.5. The answer appears straight away, with the working drawn underneath and every step written out. Whole numbers and decimals both work, with up to four decimal places, and negative numbers too.

The lattice is drawn for numbers of up to eight digits each. The Method menu switches to the column method or the area model for the same sum.

Draw a grid with a column for each digit of the first number and a row for each digit of the second. Write the first number across the top and the second down the right side. Draw a diagonal through every box, from the top right corner to the bottom left.

In each box, multiply the digit above it by the digit beside it. Write the tens above the diagonal and the ones below, so 4 × 3 = 12 goes in as 1 and 2, and 2 × 3 = 6 goes in as 0 and 6.

Then add along the diagonal strips, starting at the bottom right. If a strip adds up to 10 or more, write the ones digit and carry the tens into the next strip up. The answer is read down the left side and along the bottom, and a 0 at the very front is dropped.

Each diagonal strip holds digits of the same place value. The bottom-right strip is ones, the next is tens, then hundreds, so adding along a strip is the same as adding a column in the column method. The lattice just writes every digit product separately, so you never have to carry while multiplying, only while adding.

The method is old. It was used by mathematicians in the medieval Islamic world, came to Europe through Fibonacci's Liber Abaci in 1202, and was popular in Renaissance Italy, where it was called gelosia, after the lattice window screens it looked like. Napier's bones, from 1617, are a set of rods that carry the same grid.