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## Arithmetic (all content)

### Course: Arithmetic (all content) > Unit 3

Lesson 7: Multi-digit multiplication- Multiplying 2-digit by 1-digit
- Multiplying 3-digit by 1-digit
- Multiply without regrouping
- Multiplying 3-digit by 1-digit (regrouping)
- Multiplying 4-digit by 1-digit (regrouping)
- Multiply with regrouping
- Multiplying 2-digit numbers
- Multiplying 2-digit by 2-digit: 36x23
- Multiplying 2-digit by 2-digit: 23x44
- Multiply 2-digit numbers
- Multiplying multi-digit numbers
- Multi-digit multiplication

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# Multiplying multi-digit numbers

Sal shows lots of examples for how to multiply 2- and 3-digit numbers using "standard algorithm". Created by Sal Khan.

## Want to join the conversation?

- why did math start(57 votes)
- The only reason mathematics is admirably suited describing the physical world is that we invented it to do just that. ... If the universe disappeared, there would be no mathematics in the same way that there would be no football, tennis, chess or any other set of rules with relational structures that we contrived.(7 votes)

- Why do we use multiplication? And why do we use division?(18 votes)
- @will.wettstein we use division and multiplication in everyday life like if you are a banker or a cashier(2 votes)

- Am I supposed to multiply 3 digits by 2 (or 3) digits in my head?(5 votes)
- You can, but I suggest you stick with paper and pencil for while and put the calculator away. Calulators will give you answers, but you will learn much faster without it. If you want to see different ways of manipulating numbers, google Vedic maths.(10 votes)

- Sal sometimes is confusing me. I'm used to doing it different ways. Please help me understand his way! please!! :0 :9(7 votes)
- always keep trying one day maybe you can help someone like how you need help (o゜▽゜)o☆(3 votes)

- I hate the fact that I go in circles and I never get passed this.(5 votes)
- There is a Vedic math trick for multiplying any multi-digit numbers, called vertical and crosswise.

For example, let’s use this trick on the last problem in the lesson, 523 x 798.

Multiply the first digits: 5 x 7 = 35. This represents 35 ten-thousands.

Cross multiply the first two digits by the first two digits: (5x9)+(2x7) = 45+14 = 59. This represents 59 thousands. So we have a running total of 350+59 = 409 thousands so far.

Cross multiply the first three digits by the first three digits: (5x8)+(2x9)+(3x7) = 40+18+21 = 79. This represents 79 hundreds. So we have a running total of 4,090+79 = 4,169 hundreds so far.

Cross multiply the last two digits by the last two digits: (2x8)+(3x9) = 16+27 = 43. This represents 43 tens. So we have a running total of 41,690+43 = 41,733 tens so far.

Finally, multiply the last digits: 3x8 = 24. This represents 24 ones. So we get a final total of 417,330+24 = 417,354.

So 523 x 798 = 417,354.

If you google Vedic math, you might find some more cool arithmetic tricks!

Have a blessed, wonderful day!(7 votes)

- why does this take so long and is there a faster way to do it?(5 votes)
- Yes, there are faster ways of multiplying multi-digit numbers. Try looking up Vedic multiplication. There is a general method called vertical and crosswise, which is much faster than the usual method when the numbers have several digits. There are also fast Vedic multiplication tricks for special cases, for example when both factors are near the same power of 10.(3 votes)

- Is there in inverse operation to subtraction?(0 votes)
- Yes. If subtraction is the inverse operation to addition, then addition is the inverse operation to subtraction. It's pretty simple if you think about it!(2 votes)

- why did you just dint add to chek your work(4 votes)
- If people invented and like multiplication then why did people invent the calculator(4 votes)
- to make multiplication
**easier**(2 votes)

- How do you display this(4 votes)

## Video transcript

We now have the general
tools to really tackle any multiplication problems. So in this video I'm just going
to do a ton of examples. So let's start off with--
and I'll start in yellow. Let's start off
with 32 times 18. Say 8 times 2 is 16. Well, I'll do it in our head
this time because you always don't have all this
space to work with. So 8 times 2 is 16. Put the 1 up there. 8 times 3 is 24. 24 plus 1 is 25. So 8 times 32 was 256. Now we're going to have to
multiply this 1, which is really a 10, times 32. I'll underline it
with the orange. 1 times 2-- oh, we have
to be very careful here. 1 times 2 is 2. So you might say hey, let
me stick a 2 down there. Remember, this isn't a 1. This is a 10, so we have
to stick a 0 there to remember that. So 10 times 2 is 20. Or you say 1 times 2 is 2, but
you're putting it in the 2's place, so you still get 20. So 10 times 2 is 20. It works out. Then 1 times 3. And we have to be very careful. Let's get rid of what
we had from before. 1 times 3 is 3. There's nothing to add
here, so you just get a 3. And so you get 10
times 32 is 320. This 1 right here, that's a 10. 10 plus 8 is 18. So now we just add
up the two numbers. You add them up. 6 plus 0 is 6. 5 plus 2 is 7. 2 plus 3 is 5. Let's keep going. Let's do 99 times 88. So a big number. 8 times 9 is 72. Stick the 7 up there. And then you have
8 times 9 again. 8 times 9 is 72, but now
you have the 7 up here. So 72 plus 7 is 79. Fair enough. Now we're done with this. Let's just delete it just so
that we don't get confused in our next step. In our next we're going to
multiply this 8 now times 99. But this 8 is an 80. So let's stick a 0 down there. 8 times 9 is 72. Stick a 7 up there. Then 8 times 9 is 72. Plus 7 is 79. 2 plus 0 is 2. Let me switch colors. 9 plus 2 is 11. Carry the 1. 1 plus 7 is 8. 8 plus 9 is 17. Carry the 1. 1 plus 7 is 8. 8,712. Let's keep going. Can't do enough of these. All right, 53 times 78. I think you're getting
the hang of it now. Let's multiply 8
times 53 first. So 8 times 3 is 24. Stick the 2 up there. 8 times 5 is 40. 40 plus 2 is 42. Now we're going to have to
deal with that 7 right there, which is really a 70. So we got to remember
to put the 0 there. 7 times 3, and let's
get rid of this. Don't want to get confused. 7 times 3 is 21. Put the 1 there and
put the 2 up here. 7 times 5 is 35. Plus 2 is 37. Now we're ready to add. 4 plus 0 is 4. 2 plus 1 is 3. 4 plus 7 is 11. Carry the 1. 1 plus 3 is 4. 4,134. Let's up the stakes
a little bit. So let's say I had
796 times 58. Let's mix it up well. All right, so first we're just
going to multiply 8 times 796. And notice, I've thrown in
an extra digit up here. So 8 times 6 is 48. Put the 4 up there. 8 times 9 is 72. Plus 4 is 76. And then 8 times 7 is 56. 56 plus 7 is 63. I'm sure I'll make a
careless mistake at some point in this video. And the goal for you is to
identify if and when I do. All right, now we're ready,
so we can get rid of these guys up here. Now we can multiply this 5,
which is in the 10's place. It's really a 50. Times this up here. Because it's a 50 we
stick a 0 down there. 5 times 6 is 30. Put the 0 there, put
the 3 up there. 5 times 9 is 45. Plus the 3 is 48. 5 times 7 is 35. Plus 4 is 39. Now we're ready to add. 8 plus 0 is 8. 6 plus 0 is 6. 3 plus 8 is 11. 1 plus 6 is 7. 7 plus 9 is 16. And then 1 plus 3 is 4. So 796 times 58 is 46,168. And that sounds about right
because 796-- it's almost 800. You know, which
is almost 1,000. So if we multiplied 1,000
times 58 we'd get 58,000. But we're multiplying something
a little bit smaller than 1,000 times 58, so we're getting
something a little bit smaller than 58,000. So the number is in
the correct ballpark. Now let's do one more here
where I'm really going to step up the stakes. Let's do 523 times-- I'm going
to do a three-digit number now. Times 798. That's a big
three-digit number. But it's the same
exact process. And once you kind of see the
pattern you say, hey, this'll apply to any number of digits
times any number of digits. It'll just start taking you a
long time and your chances of making a careless mistake are
going to go up, but it's the same idea. So we start with 8 times 523. 8 times 3 is 24. Stick the 2 up there. Now 8 times 2 is 16. 16 plus 2 is 18. Put the 1 up there. 8 times 5 is 40. Plus 1 is 41. So 8 times 523 is 4,184. We're not done. We have to multiply times
the 90 and by the 700. So let's do the 90 right there. So it's a 90, so we'll
stick a 0 there. It's not a 9. And let's get rid of
these guys right there. 9 times 3 is 27. 9 times 2 is 18. 18 plus 2 is 20. And then we have
9 times 5 is 45. 45 plus 2 is 47. I don't want to
write that thick. 47. Let me make sure I did that
one right, and let's just review it a little bit. 9 times 3 was 27. We wrote the 7 down here
and put the 2 up there. 9 times 2 is 18. We added 2 to that,
so we wrote 20. Wrote the 0 down there
and the 2 up there. The 9 times 5 was 45. Plus 2 is 47. You really have to make sure
you don't make careless mistakes with these. Then finally, we have to
multiply the 7, which is really a 700 times 523. When it was just an 8 we just
started multiplying here. When it was a 90, when we
were dealing with the 10's place, we put a 0 there. Now that we're dealing with
something that's in the 100's, we're going to
put two 0's there. And so you have 7-- and let's
get rid of this stuff. That'll just mess us up. 7 times 3 is 21. Put the 1 there. Stick the 2 up there. 7 times 2 is 14. 14 plus our 2 is 16. Put the 1 up there. 7 times 5 is 35. Plus 1 is 36. And now we're ready to add. And hopefully we didn't make
any careless mistakes. So 4 plus 0 plus 0. That's easy. That's 4. 8 plus 7 plus 0. That's 15. Carry the 1. 1 plus 1 plus 1 is 3. 4 plus 7 plus 6. That's what's? 4 plus 6 is 10. It's 17. And then we have 1 plus 4 is 5. 5 plus 6 is 11. Carry the 1. 1 plus 3 is 4. So 523 times 798 is 417,354. Now we can even
check to make sure. And so this is the
moment of truth. Let's see if we
have-- let's see. 523 times 798. There you go. Moment of truth. I don't have to
re-record this video. It's 417,354. But we did it without the
calculator, which is the important point.