The Lattice Method of Multiplication
Math
Math demonstration on the Lattice Method of Multiplication
This is the lattice method of multiplication. First I will show you how to do it. Then we'll talk about why it works. Let's say we want to multiply 36 times 12. There are two digits in each of the numbers that I want to multiply. So I need to set up a box to by two. And then in each cell or each box inside the table, I draw a diagonal line. What I'm really thinking about are tens and ones, three and the one are in the tens place 6 and the two are in the ones place. That will be important later. So the next step is to write three above one box 6 above the other, and the same thing with 12. And now I simply multiply.
I can look at the numbers in any order I want because I'm only concerned with two numbers in the box that they match up at. So three times one is three. I write a zero in the top and a three in the bottom. 6 times one is 6. I write a zero in the top and a 6 in the bottom. Three times two is 6 also. So once again, where they meet up, I write a zero and a 6. And finally, 6 times two is 12. This time I write a one in the top box and a two in the bottom to show 12. Then I look at them and add diagonally. I'm adding this way. This way. This way, and this way. So two plus nothing is two. 6 and 6 and one are 13. But just like in addition, I put my three here and carry a one to the next column. One and three and two zeros are four. And zero plus nothing is zero. So then I look at my answer this way to see that it's 432. So the answer to 36 times 12 is 400 32.
The reason this works is because of this. When I multiplied 6 times two, I was multiplying the ones times the ones, so 6 times two is 12. I put the two in the ones column. And I put the one in the tens column. This is the tens column. Next I did 6 times one, but really, that's like ten because this is one in the tent column for 12. It's the one here, so it's like ten. So 6 times ten is really 60. So I'm putting the 6 in the tens column here. This is the tens column. The next thing I did was three times two, but it's really like 30 times two. 30 times two is 60. So it's really 6 tens. The next thing I did, plus three times one, but it's really like saying 30 times ten. 30 times ten is 300. So this is my next column, and it's the hundreds column.
All of the things here represent hundreds. So then when I add it up, I'm adding up two ones. 6 6 and one tens, which means 1310s, or a 130. I'm going to write my three tens and the tens column and I'm going to carry my 100 to the hundreds and add that hundred plus 300s to get 400s. So the answer is 400 32. And that works because I lined up all of my ones, all of my tens, and all of my hundreds.