Dividing 4 digit by 2 digit numbers using partial quotients

0:00- [Instructor] Let's say we wanted to figure out what 3,968 divided by 32 is. And there's many different ways that we can approach this, but we're going to use a technique known as partial quotients, and I know that sounds very fancy, but we're about to see it's actually a pretty fun and even maybe forgiving way of doing division.

0:25So what do I mean by that? So let me rewrite this as 3,968 divided by 32. Now, what you wanna do is think about how many times can 32 go into this number without going over it, and I like to use numbers that are easy to do in my head. So I could think about, well, let's see, 32 times 10 would be 320.

0:50That could work. I could even do 32 times 100, and that would get to 3,200, which is still less than this, so let me work that out. So if I did, let me write this. So if I, I'll do it in another color here. If I said 32 times 100, this is going to be 3,200. So that doesn't go over it.

1:12So let me write that here, and you're about to see what I do here. So I know I can go 32 times, but I could go more than 32 times, but 32 times gets me 3,200 of the way there. So what's left over? So now I just subtract, and if I subtract 3,000, or if I subtract 3,200 from 3,968, I am going to get eight minus zero is eight, six minus zero is six, nine minus two is seven, and then the thousands cancel out.

1:39So now it all boils down to how many times can 32 go into 768? Well, let's think about this for a second. If I said, well, let's say 10 times, so 32 times 10, 32 times 10 is equal to 320. That doesn't go above 768. So let's subtract 320 from here, and now, what do I have left?

2:04Eight minus zero is eight, six minus two is four, seven minus three is four. Well, this is interesting, because 320 still goes into this. So let me try this. Let me now think about 32 times 10 again, which is going to be 320. So I'm gonna go 10 more times. So that's going to be another 320.

2:26Let me subtract. Eight minus zero is eight, four minus two is two, and then four minus three is one. Now, here, you might be able to say, "Well, you know, this looks like 30 times four is 120, "so maybe 32 times four works out." Let's try that out. So if I were to say 32 times four, this is going to be what?

2:51It's going to be 30 times four plus two times four, which would be 128. So this one works out. 100, this is gonna be equal to 128. I subtract, and I have nothing left over. So what does this equal? What does 3,968 divided by 32 equal? Well, you can see I was able to get 100 32s in there, then another 10, then another 10, and then another four.

3:17So if I add up 100 plus 10 plus 10 plus four, what do I get? Let's see, 10 plus 10 is 20 plus four is 24 plus 100 is 124. This is equal to 124. Now, this isn't the only way that I could've done this, as I could've said, let me do this over here. Actually, let me just delete this and show you another way I could've done this.

3:41Let me delete all of this business here. And I'll leave that 124 there since we already know that's the answer, but I wanna show you there's another way I could've gotten there. Actually, let me just delete that too, just so you can see that. So I could've started saying, well, let's say, let me see, 32, maybe it goes into 3,968.

4:02Actually, I could've started with 10. I could've said 10 times 32 is, 10 times 32 is equal to 320. So I put a 320 there. I'm not chipping away a lot this time, but then when I subtract eight minus zero is eight, six minus two is four, nine minus three is six, and then bring down that three thousands, this is how much I have left.

4:26And now I could say, well, let me try to go a little bit more, maybe I could go 50 times, and I'm just making up things here. So if I said 50 times 32, what is that going to be equal to? Well, let me see, 32 times 50, let's see, 32 times five is, two times five is 10, five times three is 15 plus one is 16.

4:53So 32 times five is 160. 32 times 50 is 1,600. So that's equal to 1,600. And so, if I were to put this 1,600 here, I subtract again, eight minus zero is eight, four minus zero is four, I get a zero, I get 2,048, and I could keep going. Now, let's see, 32 goes into 2048, well, I could go another 50 times.

5:1850 times 32 is equal to 1,600. And so, let me write that here, 1,600. I subtract, and let's see. This becomes what? Eight minus zero is eight, four minus zero is four, 20 minus 16 is four, so 448. And let's say I wanna, well, let me just go another 10 times. So 32 times 10 is equal to 320.

5:49320, I subtract. I get the 128, and then we've seen that if I do 32 times four, that is equal to 128. So 128, and I could subtract now and get to a remaining, I know I'm going off the screen here, but let me do it. Maybe I could do it like this. Let me move this up a little bit.

6:09If I subtract now, I get zero, and if I were to add 10 plus 50 plus 50 plus 32, sorry, 10 plus 50, the thing multiplying by 32 plus 50 plus 10 plus four, that gets me, this is 124. Once again, 124. So there's multiple ways that you could do partial quotients division, or long division depending on how you wanna think about it, and it's really nice, because as long as you chip away a little bit without going over, you're able to keep going, and keep getting at what the final quotient is going to be.