Multiplying multiple digit numbers | Multiplication and division | Arithmetic | Khan Academy
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Multiplying multiple digit numbers | Multiplication and division | Arithmetic | Khan Academy

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.

About James Carlton

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94 thoughts on “Multiplying multiple digit numbers | Multiplication and division | Arithmetic | Khan Academy

  1. To do it in Hex, you would have to memorize your 16 times tables in hex (and convert to and from decimal to hex). Would take up less space on the paper. Not clear if it would be easier.

  2. When doing the 99×88 Sum, Why when doing the first 9×8 does he put down the 2 and carry on the 7… I always though you carried on the smallest number and put down the largest…. That's really confusing me ;(

  3. If you actually know what hexadecimal is, then why are you watching a video about multiplying multiple-digit numbers?

  4. What your actually doing is multiplying every number with every other number, but your teachers don't want you to know this because you might accidently remember it when you get to combination theory and multiplying binomials.

  5. that's how my mom taught me 53 years ago. I'm becoming more & more convinced that my folks had something up their sleeve that worked & turned out geniuses, thii they were destroyed by the invasion by the west. & Mr. Khan & I share the same heritage & genetic material as far as the geographi specificity of the DNA is concerned.

  6. Thank you so much!^^ This will hopefully help me for my.exam tomorrow!:) I gotta watch this video again when I'm at school waiting to get into class.

  7. Frankie O'B, this is a late reply and not even directly to your comment since YouTube apparently thought that was a bad idea, but let me answer your question anyway. What you actually are doing is carry the biggest number, because you carry it to the next place — e.g. from the ones place to the tens place. The 7 that you're carrying actually represents 7 tens, as it comes from 72 which is 70 + 2. So you leave the 2 in the ones place where it belongs, and you put the 7 in the column for the tens place.

    You probably got confused because you got a lot of 6*3 and 5*5 where you get answers like 18 and 25, where the first number (the tens, the one that you carry) is smaller than the second (the ones, the one that you leave in place). Since tens are bigger, they often times go up less quickly, after all. Just remember that the actual rule is to carry the number for the biggest 'place' (tens over ones, hundreds over tens). Technically, in that sense, you're always carrying the BIGGEST number — 70 rather than 2, 10 rather than 8, or 20 rather than 5.

    Hope that helps.

  8. Thank you so much, I finally get how to multiply triple digits! I kept getting the wrong answer but I went step by step and I got the write answer

  9. Your the best Mr Khan you helped my daughter so much ever since she's been watching her videos. Mr Khan I don't know what I could do without you.


  11. thanks dude i never new how to do this it would take me forever to do this and i would cry if i got it incorect and also get realy angry your the best dude

  12. thanks idid not understand then i got just looking at your name tag THANKS YOOOOOOOOOUUUUUUUUUU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  13. I just found you thanks to a friend’s recommendation. With this video you helped me understand 3 digits multiplication I’ve never understood in school! I’m 36 😂 thank you and please don’t ever stop what you’re doing, amazing work!! You have a new subscriber 😀

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