Everyday Math: The Lattice Method

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The "Lattice" method is related to long multiplication problems. Find out about the Lattice method and learn what it does with help from a longtime mathematics educator in this free video clip.

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Hi, I'm Jimmy Chang, and we're here to talk about everyday math, the lattice method. Now the lattice method is alternatively an alternative method to long multiplication so if you wanted to multiply numbers and you wanted to think about a method that uses something other than the conventional long multiplication method of multiplying, carryover, etc., then you might want to think about trying this one. So we're going to do an example on a two digit number, multiplying by a two digit number but understand that you can extend this to a three digit and so on and so forth. So suppose you wanted to find out let's just say 21 times 17, okay. So first of all what you want to do is because you have a two digit times a two digit number, you'll want to create a two by two, you can think of it kind of like a matrix type shape but it's basically, think of it as a square with four squares and there are two columns and two rows and what you want to do after that is create diagonals as a result. So you have a diagonal here, a diagonal from this corner to this corner and then another diagonal from this corner to this corner. Now what does this have to do with the numbers themselves? Well this actually gives you some placement in terms of what numbers go where. So because 21 was mentioned first, 21 would be over here and then 17 is going to be here. Okay, now, the way this method works is part of it as you can tell is the set up. Now, once you've put the numbers where they belong and after you have drawn the diagonals going forward, this is where the multiplication takes place. So first let's just start with the 1 and multiplying by what you see here. Now 1 times 1 as you know is 1. Now you may notice there's two slots here but 1 times 1 because it's just a one digit number, you want to write it as a "two digit number". In other words, 0 1, because that's what 1 times 1 is. Now when it comes to 1 times 7, it's the same kind of idea because 1 times 7 is 7 but because you want to write it as a "two digit number" you'll write it as 0 7. So you want to repeat with the 2, 2 times 1 is going to be 2. So it's going to be 0 2. Now this is where things become a little more interesting because when you have 2 times 7 you have 14. So now you have a true two digit number so it will be 1 4 like so. Now, in terms of getting to the final answer this is where you start adding some numbers throughout the diagonal. So what you're going to do is you're going to add the numbers starting from the bottom, working our way to the top. So in other words we're going to look at this diagonal, as you can tell, there's only one number here so you're going to put the final answer here. Now, for this diagonal you're going to add 1 plus 0 plus 4 and as you know, that is 5. Now, just as a note if you happen to add these three numbers and you have a number that is bigger than 10 what you're going to do is you would have written the 0 here and carry over the 1 at the very top of this following layer of diagonal and then continue adding. So just make that adjustment if you need it. So but in this case because the number we have is less than 10, you wouldn't have to worry about that here. Now we're going to continue by adding the numbers along this diagonal, 0 plus 2 plus 1 which is going to be 3 and then lastly, over here when you add this number obviously that's just a 0. So basically in terms of the final answer, you actually look at it this way, you start here and then you end over here. So you start at this corner and then you have a little path going and as you can tell, it's going to be 0, 3, 5, 7 which means that actually the final answer is 357. So 21 times 17 is 357. So if you follow this method and the steps you should be good to go when it comes to following this particular approach and it's kind of a fun approach after a while. So I'm Jimmy Chang and that's a brief overview into everyday math, the lattice method.

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