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## 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 4-digit by 1-digit (regrouping)

Learn to multiply a 4-digit number by a 1-digit number. In this video, we will multiply 8085 times 9. Created by Sal Khan.

## Want to join the conversation?

- can u do the same thing or concept for billion(4 votes)
- Yes you can. The possibility of multiplying different numbers is infinite.(7 votes)

- why are there negitive numbers?(4 votes)
- You can imagine that negative numbers mean something owed. It's not that you can hold negative something, but rather you need to take that number from something else. For example I have 25 apples and you want 5. So 25-5 = 25 + (-5) represents you taking the 5 from me.(6 votes)

- I'm surprised no one uses this for chat(6 votes)
- so 5x2 is like 2+2+2+2+2 so 5x2=10 so 2+2+2+2+2 ok i can do that?(5 votes)
- Yes. That is a common strategy for multiplication.(0 votes)

- if you change the places will you need to do more work then you orignaly did (im bad at spelling sorry)(4 votes)
- Yep! It's ok that you aren't good at spelling as long as others can understand you, and I can.(3 votes)

- i need to learn my fact in my head(4 votes)
- That's what i do but it gets diffucult in your head and it messes up the problem(2 votes)

- Do you sometimes need to divide when you're regrouping,or is it just plain multiplying?(3 votes)
- the multi digit multiplication is so easy and now i under stand it better than before.(1 vote)
- What exactly is the "regrouping" in the video title? What is being regrouped?(1 vote)
- At0:30, he multiplies 9X5, which is 45. That is 4 tens and 5 ones. The 5 is written and the 4 (40) is carried to the next column. He then multiplies 9X8, which is 72, but because the 8 is in the tens place, it's really 9X80, so the result is 720. But then you have to add in the 40 from the previous step, which he wrote in above as a reminder. 720 + 40 = 760, so he writes a 6 in the tens place, there are no ones so that doesn't change, then he carries the 7 hundreds over to the hundreds column.

When he adds in the additional value carried over from the previous step, that is the regrouping.(0 votes)

- What does the trascript thing mean?(2 votes)
- The transcript is basically the script for the video, everything Sal says that's important.(0 votes)

## Video transcript

Let's multiply 9 times 8,085. That should be a pretty fun
little calculation to do. So like always, let's
just rewrite this. So I'm going to write the 8,085. I'm going to write
the 9 right below it and write our little
multiplication symbol. And now, we're ready to compute. So first we can
tackle 9 times 5. Well, we know that
9 times 5 is 45. We can write the 5
in the ones place and carry the 5
to the tens place. So 9 times 5 is 45. Now we're ready to
move on to 9 times 8. And we're going to
calculate 9 times 8 and then add the 4
that we just carried. So 9 times 8 is 72,
plus the 4 is 76. So we'll write the 6 right here
the tens place and carry the 7. Now we are ready to
calculate, and I'm looking for a suitable color. 9 times 0 100's plus-- and this
is a 7 in the hundreds place, so that's actually 700. Or if we're just kind of
going with the computation, 9 times 0 plus 7. Well, 9 times 0
is 0, plus 7 is 7. And then, finally, we
have-- and once again, I'm looking for a suitable
color-- 9 times 8. This is the last thing
we have to compute. We already know that
9 times 8 is 72. And we just write the 72 right
down here, and we're done. 8,085 times 9 is 72,765. Let's do one more
example just to make sure that this is really clear
in your brain, at least the process for doing this. And I also want you to
think about why this works. So let's try 7 times 5,396. And I encourage you to pause it
and try it on your own as well. I'm going to rewrite
it-- 5,396 times 7. First, we'll think
about what 7 times 6 is. We know that's 42. We'll put the 2
in the ones place. 4 we will carry. Then we need to concern
ourselves with 7 times 9. But then, we have to calculate
that and then add the 4. 7 times 9 is 63, plus 4 is 67. So we put the 7 down
here and carry the 6. Then we have to worry
about 7 times 3 plus this 6 that we had just
finished carrying. 7 times 3 is 21, plus 6 is 27. So we'll write the 7 here in the
hundreds place and carry the 2. And then, finally, we have
7 times 5, which is 35. But we have to add the 2. 35 plus 2 is 37. So 5,396 times 7 is 37,772.