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I'm going to do a couple of lattice multiplication

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examples in this video.

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And in the next one we'll try to understand why it worked.

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Let's say we're trying to multiply 27 times 48.

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What you do is you write down your 27.

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The 2 and the 7 are going to get separate columns and you

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write your 48 down the right-hand side, and then

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you draw a lattice.

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This is why it's called lattice multiplication.

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So the 2 is going to get its own column.

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The 7 is going to get its own column.

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The 4 is going to get its own row and the 8 is

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going to get its own row.

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Now the fun thing about lattice multiplication is you get to do

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all of your multiplication at one time and then you can

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finish up the problem with all your addition.

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You don't have to keep switching gears by

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carrying and all of that.

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Although there is carrying, but it's all while you're

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doing the addition step.

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So we're almost done with our lattice.

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We actually have to draw these diagonals here.

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We'll understand in the next video why these

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diagonals even work.

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Just like that.

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And now we're ready to multiply.

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7 times 4 is 28.

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7 times 4 is equal to 28.

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So you write down a 2 and an 8 just like that.

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2 times 4 is equal to 8.

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So you write down a 0, 8 just like that.

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Then you have 7 times 8.

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7 times 8 is equal to 56.

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So we write down a 5 and a 6.

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And then finally, 2 times 8 is equal to 16.

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You write down a 1 and a 6 just like that.

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And we're done all of our multiplying.

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Now we're ready to add.

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So what you do is you go down these diagonals

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that I drew here.

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So this first diagonal, which is really the 1's diagonal, you

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just have a 6 sitting here.

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So you write a 6 just like that.

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Then we move over to the next diagonal.

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This diagonal with the 6, 5, and 8 in it.

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That's our 10's diagonal.

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So 8 plus 5 is 13.

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13 plus 6 is 19.

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So you write your 9 right here in the 10's place and now you

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carry the 1 in 19 up there into the 100's place because this

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isn't just 19, it's actually 190.

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It's nineteen 10's.

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Anyway, you carry your 1.

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You have 1 plus 2 is 3.

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3 plus 8 is 11.

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11 plus 1 is 12.

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You write the 2 in your 100's place and you carry the 1

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into your 1,000's place.

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1 plus 0 is 1, so you just have a 1 in your 1,000's

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place just like that.

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And you get our answer.

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27 times 48 is equal to 1,296/ Let's do a harder problem.

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One that requires more digits, just to show that this'll

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work for any problem.

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Let's say we had 5,479 times-- let's do a three-digit number.

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Times 787.

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So just like we did in the last time, we make four columns.

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One for the 5, the 4, the 7, and the 9.

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We'lll have 5,479 and then times 787.

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So they each get their own row.

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787.

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Looks like that.

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Then we have to draw our lattice.

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Draw the lattice.

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Each of these guys get their own column.

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Draw the columns just like that.

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And then each one of these characters got their own row.

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One row for the 7, one row for the 8, and one

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row for this other 7.

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Then we have to draw the diagonals.

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Draw it like that.

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One diagonal, two diagonals, so three diagonals,

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four diagonals.

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I think you get the idea and than we have just

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one, two more diagonals.

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We're ready to multiply now.

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So it's 9 times 7.

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I won't do it on the side here.

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We know our times tables.

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9 times 7 is 63.

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7 times 7 is 49.

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4 times 7 is 28.

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5 times 7 is 35.

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Let me switch callers arbitrarily.

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9 times 8 is 72.

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7 times 8 is 56.

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4 times 8 is 32.

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5 times 8 is 40.

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I'll switch colors again.

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9 times 7-- we saw that before.

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It's 63.

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7 times 7 is 49.

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4 times 7 is 28.

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And then 5 times 7 is 35.

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We're done all of our multiplying.

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Now we can switch our brains into addition mode.

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Let me find a nice suitable color for addition.

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Maybe a pink will do for addition.

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So we start at our 1's place.

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Just have a 3 there, so you write the 3 in your 1's place.

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You go to the 10's place.

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2 plus 6 is 8.

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8 plus 9 is 17.

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Write the 7 in the 10's place, carry the 1

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into the 100's place.

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I wrote a 1 really small here.

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1 plus 3 is 4.

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4 plus 7 is 11.

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11 plus 6 is 17.

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17 plus 4 is 21.

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21 plus 8 is 29.

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Write the 9 in the 100's place and carry the 2.

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2 plus 6 is 8.

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8 plus 9 is 17.

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17 plus 5 is 22.

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22 plus 2 is 24.

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24 plus 2 is 26.

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26 plus 5 is 31.

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Carry the 3.

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3 plus 4 is 7.

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7 plus 8 is 15.

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15 plus 3 is 18.

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18 plus 0 is 18.

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18 plus 3 is 21.

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Write the 1, carry the 2.

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2 plus 2 is 4.

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4 plus 5 is 9.

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9 plus 4 is 13.

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Write the 3, carry the 1.

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1 plus 3 is 4.

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And we're done.

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That easy.

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Well, there's two advantages here.

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One is we got to do all of our multiplication at once.

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And then we got to do all of our addition at once.

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The other advantage is it's kind of neat and clean.

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When you just do it the traditional way with carrying

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and number places, it takes up a lot of space.

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But notice, we did our whole problem in a nice, neat

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and clean area like that and we got our answer.

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Our answer is 4,311,973.

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There you go.

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Now in the next video we're going to try to understand

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why this worked.