Another multiplication trick

This isn't so much a trick as it is an aid to getting all your numbers to line up when multiplying large numbers. I mean there's all that jazz about adding extra zeroes and making sure your handwriting is good enough so everything is in the proper columns. You get students who do all the math right, but get the wrong answer due to alignment (I'm lawful chaotic) issues.

Say you have two rather large numbers to multiply together. For this example I'm gonna use 8,675,309 and 31,009. This trick doesn't really change what you have to do to get the answer. It just formats it different and makes it easier to line everything up. It requires you knowing more math than the Russian Peasants did.

First you need to draw a grid like this. One of the two numbers runs across the top and the other down the side.

What you're going to eventually do is multiply all the numbers and write them in the grids where those two numbers cross. Tens go on the upper left and the ones in the lower right.

Lets get the easy stuff out of the way first. Zero times anything is still zero. Fill in all the rows and columns where there's a zero.

Anything times one is easy, too.

Fill in the rest.
Starting in the upper left where the row is 3 and the column is 8. 3 x 8 = 24. Two in the upper left, four in the lower right. You get the idea.


Now add up all the numbers in each diagonal... um... thingy. Slice? I've highlighted them to make it more obvious. Don't forget to carry the tens place to the next number.

That's a doozy of a number.
You can check it by Googling "8675309 * 31009 =".