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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.

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  • starky tree style avatar for user Damian
    why did math start
    (57 votes)
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    • female robot ada style avatar for user Tarunya Mahesh
      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)
  • winston baby style avatar for user will.wettstein
    Why do we use multiplication? And why do we use division?
    (17 votes)
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  • leaf red style avatar for user Nicola
    Am I supposed to multiply 3 digits by 2 (or 3) digits in my head?
    (5 votes)
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  • duskpin ultimate style avatar for user Kiera <3 J Moore
    Sal sometimes is confusing me. I'm used to doing it different ways. Please help me understand his way! please!! :0 :9
    (7 votes)
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  • duskpin sapling style avatar for user alittlejohn
    I hate the fact that I go in circles and I never get passed this.
    (5 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      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)
  • leafers sapling style avatar for user soniakennedy28
    why does this take so long and is there a faster way to do it?
    (5 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      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)
  • aqualine ultimate style avatar for user wespinel
    Is there in inverse operation to subtraction?
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  • old spice man blue style avatar for user omarion washington
    why did you just dint add to chek your work
    (4 votes)
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  • hopper happy style avatar for user 6
    If people invented and like multiplication then why did people invent the calculator
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  • duskpin sapling style avatar for user sajedlinski
    How do you display this
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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.