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# Lattice multiplication

## Video transcript

I'm going to do a couple of lattice multiplication examples in this video and the next one will try to understand why it worked so let's say we're trying to multiply 27 times 48 what you do is you write down your 27 the 2 and the 7 are gonna get separate columns and you multi-multi your 48 down the right-hand side and then you draw a lattice this is why it's called lattice multiplication so the 2 is going to get its own column the 7 is going to get its own column the 4 is going to get its own row and the 8 going to get its own row now the fun thing about lattice multiplication is you get to do all of your multiplication at one time and then you can finish up the problem with all your addition you don't have to keep switching gears by carrying and all of that although there is carrying but it's all while you're doing in the addition step now we're almost done with our lattice which you have to draw these diagonals here we'll understand in the next video why these diagonals even work just like that and now we're ready to multiply 7 times 4 is 28 7 times 4 is equal to 28 so you write down a 2 and an 8 just like that 2 times 4 2 times 4 is equal to 8 so you write down a 0 8 just like that then you have 7 times 8 7 times 8 is equal to 56 so we write down a five and a six and then finally 2 times 8 2 times 8 is equal to 16 so you write down a 1 and a 6 just like that and we're done all of our multiplying now we're ready to add so what you do is you go down these these diagonals that I drew here so this first diagonal which is really the one's diagonal you just have a 6 sitting here so you write a 6 just like that then we move over to the next diagonal this diagonal with the 6 5 and 8 in it that's our tens diagonal so 8 plus 5 is 13 13 plus 6 is 19 so you write your 9 right here in the tens place and now you carry the 1 and 19 up there into the hundreds place because this is just 19 it's actually 1 290th 1910s anyway you carry your 1 you have 1 plus 2 is 3 3 plus 8 is 11 11 plus 1 is 12 you write the 2 in your hundreds place and you carry the 1 into your thousands place 1 plus 0 is 1 so you just have a 1 in your thousands place just like that and you get our answer 27 times 48 is equal to one thousand two hundred and ninety-six 1296 let's do a harder problem one that requires more digits just to show that this will work for any problem let's say we had five thousand four hundred and seventy nine times this to a three-digit number times 787 so just like we did in the last time we make four columns one for the five the for the seven and the nine we'll have a five thousand four hundred and seventy nine and then times 787 so they each get their own row 787 so like that then we have to draw our lattice draw the lattice each of these guys get their own column draw the columns just like that and then each of these characters get their own row one row for the seven one row for the eight and one row for this other seven then we have to draw the diagonals draw like that one diagonal two diagonals three diagonals or diagonals I think you get the idea and then we have just one two more diagonals we're ready to multiply now so it's nine times seven I won't do it on the side here we know our times tables 9 times 7 is 63 7 times 7 is 49 4 times 7 is twenty eight five times seven is thirty-five let me switch colors arbitrarily 9 times 8 is 72 7 times 8 is 56 4 times 8 is 32 5 times 8 is 40 I'll switch colors again 9 times 7 we saw that before it's 63 7 times 7 is 49 4 times 7 is 28 and then 5 times 7 is 35 we're done all of our multiplying now we can switch our brains into addition mode we find a nice suitable color for addition maybe no maybe a pink will do or addition so we started our ones place just have a three there so you write the 3 in your ones place your the tens place 2 plus 6 is 8 8 plus 9 is 17 write the 7 in the tens place carry the 1 into the hundreds place now I wrote a 1 really small here 1 plus 3 is 4 4 plus 7 is 11 11 plus 6 is 17 17 plus 4 is 21 21 plus 8 is 29 right the 9 in the hundreds place and carry the 2 2 plus 6 is 8 8 plus 9 is 17 17 plus 5 is 22 22 plus 2 is 24 24 plus 2 is 26 26 plus 5 is 30 1 is 31 carry the 3 3 plus 4 is 7 7 plus 8 is 15 15 plus 3 is 18 18 plus 0 is 18 18 plus 3 is 21 right the 1 carry the 2 2 plus 2 is 4 4 plus 5 is 9 9 plus 4 is 13 right the 3 carry the 1 1 plus 3 is 4 and weird one that easy I think well there's two advantages here one is we got to do all of our multiplication at once and then we've got to do all of our addition at once the other advantage is it's kind of neat and clean when you just do it this the traditional way with carrying and number of places it takes up a lot a lot of space but notice we did our whole problem in a nice neat and clean area like then we got our answer our answer is four million three hundred and eleven thousand nine hundred and seventy-three there you go now in the next video we're going to understand why this worked