The Lattice Method of Addition

Instructor: Michael Quist

Michael has taught college-level mathematics and sociology; high school math, history, science, and speech/drama; and has a doctorate in education.

The lattice method of addition is an alternate form of adding numbers that eliminates the need to 'carry' tens over to the next column. This lesson will explain the lattice method of addition.

What is the Lattice Method of Addition?

You want to add a column of big numbers, and you're tired of doing all that carrying that you have to do when sums get larger than 9. Is there another way to do it? Yes! If you don't mind drawing a few lines and adding in creative directions, you never have to carry a 10 (or 20 or 30 or 40) again! Let's take a look at how to do it:

1. Stack the numbers you're adding in a column, keeping all of the digits in the right places (you know, the 1's digits in the 1's place, 10's digits in the 10's place, and so on). For example, say we want to add 346, 4,567, and 23 together. First, we would stack them in a vertical column.

First we stack the numbers
stack the numbers

Once the numbers are in a stack (and all the digits are in their proper columns), then we can start the fun! First of all, we will add each column, but instead of writing the 1's digit of the result and carrying the 10's digit, we're just going to write the sums down, in a stack below the line. Walking through the process with the 1's column of numbers, we see:

Adding the numbers: 5 + 7 + 3 = 15
lattice method--adding the 1s place

Now here's the trick. We want to use a 'lattice'--a structure--to put those numbers where they belong. We'll draw a little box, with a diagonal line through it, and put our total in the box, with the 10's digit in the upper left and the 1's digit in the lower right:

We put the 15 result from adding the 1s digits into a lattice structure box
lattice method step 3

Now we'll do the same thing in the 10's place, and will put the result in a box next to the 1's box:

Adding the 10s digits, we get 12 (4 + 6 + 2 = 12), which we put in a lattice box next to the 1s
lattice step 4

Then the 100's:

Adding the 100s digits we get a total of 8 hundreds (no 10s of hundreds), so we put the 8 in the lower right and a 0 in the upper left part of the lattice box
lattice step 5

Time to pull in the 1000's digits--we have only the 4 thousands--in the 4567 number--so we don't have to add anything, we just pull him down into his own lattice box:

Bringing the only thousands digit down to its lattice box
lattice step 6

Whew! Now that we're done setting it all up, let's use this lattice thing we've created. By adding along the diagonal lines, we'll see the sum of the original three numbers appear.

There was nothing more to add along the 1s diagonal, so we just moved the 5 down to his position
lattice step 7

Finally, let's add the other guys, following the diagonal lines, down and to the left.

Adding along the diagonals produces a sum of 4,935
lattice step 8

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