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## Arithmetic

### Course: Arithmetic>Unit 8

Lesson 5: Multi-digit division with partial quotients

# Introduction to division with partial quotients (no remainder)

Sal divides multi-digit numbers by a single-digit numbers using partial quotients.

## Video transcript

- [Instructor] In this video, we wanna compute what 833 divided by seven is. So I encourage you to pause this video and see if you can figure that out on your own. All right, now let's work through it together. And you might have appreciated, this is a little bit more difficult than things that we have done in the past. And in this video, I'm going to show you a method that your parents have probably not seen, but you'll see that it's kind of fun, and it's called division with partial quotients, which is a very fancy word, but as I said, it'll be fun. So, the first thing I will do is I will rewrite this as 833 divided by, divided by seven. So you can view these as the same expression. The reason why we do it this way is it formats it so it's a little bit easier to do our division with partial quotients. So the way that division with partial quotients works, and once again, it's not the way that your parents probably learned how to do it, is you just say, hey, how many times can seven go into 833? I don't have to get it exactly. I just wanna go under 833. And so my brain immediately thinks, well, seven hundreds is less than 833, so we're going to go into 833 at least 100 times. And so what we would do is we would write that hundred up here. We'd wanna be very careful about our place value. You can view this column as the hundreds column, this is the tens column, this is the ones column, and then we wanna see, how much do we have left over? How close did seven times 100 get us? So what we do is we multiply 100 times seven to get 700, and then we can subtract that 700 from 833 to figure out how much more we have left. And so 833 minus 700 is 133. And so we can then say, all right, we still have another 133 to go. So how many more times can seven go into this? Well, seven goes into 133, once again, you don't have to have it exactly. If you know seven times 10 is equal to 70, actually, let's go with that. We know we go at least 10 times. So let's write that up here. We're going at least 10 times, and to figure out how much more we have left, let's multiply 10 times seven to get 70, and then we can subtract, and we see that we have, let's see, three minus zero is three. 13 tens minus seven tens is six tens. So we have 63 left. So seven definitely can go into 63. We're gonna keep doing this until we have a number less than seven over here. So let's see, seven, how many times does seven go into 63? You might know from your multiplication tables that seven times nine is 63. So you could get it exactly. So you could just write that up here. We have nine more times to go into the number, and then you would say nine times seven is 63. You could say, hey, we got exactly there. We have nothing left over. And as long as this number is less than seven, you know that you can't divide seven anymore into our original number. And so, you're done. And so, how many times does seven go into 833? Well, we said it went 100 times, and then we were able to go another 10 times, and then we were able to go another nine times. And so what we wanna do is add these numbers. So you wanna add 100 plus 10 plus nine. When you add up all of them, what do you get? You get nine ones, one 10, one hundred. You get 119, so this is equal to 119. All I did is I added these up. Now, I wanna be very clear that you could do division with partial quotients and not do it exactly like this. That's kind of why it's fun. So let's do it another way. So let's say we wanna figure out again how many times does seven go into 833, 833? We could have said, maybe it goes 150 times. So what you could have said is you could have said, all right, my current guess or estimate is 150 times, that I could multiply 150 times seven. How would I do that? Let's see, zero times seven is zero, five times seven is 35. You can carry the three, so to speak. One times seven is seven plus that three is going to be 10. And so that gets us to 1050. Well, over here, we just finished overshooting. It doesn't go 150 times. There's nothing left over. So 150 is too high. So we would wanna backtrack that. And then you would go, well maybe I could go to 110. So let's try that out. So 110, and now let's multiply. Zero times seven is zero. One times seven is seven. One times seven is seven. So, 110 times seven is 770. So that works. It's less than 833, but let's see what we have left. So we subtract, we get a three here, and then, let's see, 83 tens minus 77 tens, that's six tens, and actually, that got us there a lot faster. So then you could just know that hey, seven goes into 63 times. But let's say we didn't know that. We could say, all right, let's say I'm gonna estimate it goes eight times. So you would put an eight up here. And then you say, how much did we have left over? Eight times seven is 56. You subtract, and then 63 minus 56 is exactly seven. And you say, okay, look, I can go one more time. So I'd write that up there. So one times seven is seven, and then you see we have nothing left over. So we are done. So how many times did it go in? One plus eight is nine plus 110 is 119. So hopefully, you find that interesting, and I really want you to think about why this is working. We're just trying to see how many times can we go in without overshooting it, and then what's left over? So how many more times can we go in, and then what's left over, and then how many more times can we go in, until what we have left over is less than seven, so that we can't go into it any more times.