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## Multiplication: place value and area models

# Lattice multiplication

## Video transcript

I'm going to do a couple
of lattice multiplication examples in this video. And in the next one we'll try
to understand why it worked. 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 going to
get separate columns and you write 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 is 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 the addition step. So we're almost done
with our lattice. We actually 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 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 5 and a 6. And then finally, 2
times 8 is equal to 16. 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 diagonals that I drew here. So this first diagonal, which
is really the 1'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 10's diagonal. So 8 plus 5 is 13. 13 plus 6 is 19. So you write your 9 right here
in the 10's place and now you carry the 1 in 19 up there into
the 100's place because this isn't just 19, it's
actually 190. It's nineteen 10's. 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 100's
place and you carry the 1 into your 1,000's place. 1 plus 0 is 1, so you just
have a 1 in your 1,000's place just like that. And you get our answer. 27 times 48 is equal to 1,296/
Let's do a harder problem. One that requires more digits,
just to show that this'll work for any problem. Let's say we had 5,479 times--
let's do a three-digit number. Times 787. So just like we did in the last
time, we make four columns. One for the 5, the 4,
the 7, and the 9. We'lll have 5,479
and then times 787. So they each get their own row. 787. Looks 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 one of these
characters got their own row. One row for the 7, one
row for the 8, and one row for this other 7. Then we have to draw
the diagonals. Draw it like that. One diagonal, two diagonals,
so three diagonals, four diagonals. I think you get the idea
and than we have just one, two more diagonals. We're ready to multiply now. So it's 9 times 7. 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 28. 5 times 7 is 35. Let me switch callers
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. Let me find a nice suitable
color for addition. Maybe a pink will
do for addition. So we start at our 1's place. Just have a 3 there, so you
write the 3 in your 1's place. You go to the 10's place. 2 plus 6 is 8. 8 plus 9 is 17. Write the 7 in the 10's
place, carry the 1 into the 100's place. 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. Write the 9 in the 100's
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 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. Write the 1, carry the 2. 2 plus 2 is 4. 4 plus 5 is 9. 9 plus 4 is 13. Write the 3, carry the 1. 1 plus 3 is 4. And we're done. That easy. Well, there's two
advantages here. One is we got to do all of
our multiplication at once. And then we 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 the
traditional way with carrying and number places, it
takes up a lot of space. But notice, we did our whole
problem in a nice, neat and clean area like that
and we got our answer. Our answer is 4,311,973. There you go. Now in the next video we're
going to try to understand why this worked.