Division with partial quotients (remainder)

- [Instructor] Let's say we wanna figure out what 473 divided by five is. And like always, why don't you pause this video and try to work through it? And if you're familiar with the idea of division with partial quotients, I encourage you to try it out that way. All right, now let's work on this together. And so let me just rewrite this in a format that makes it a little bit easier for me to do my division with partial quotients. And so I'm just going to write 473 divided by five. And what's neat about division with partial quotients is that there's a lot of flexibility in how you do it. There's no exactly one right way. And so you could say, all right, how many times can five go into 473 without going over 473? You might be tempted. Someone might say, "Oh, maybe you can go a hundred times." But you could quickly see that if you said a hundred times, and they say, "How much do I left over?" you do a hundred times five. You get 500. And you'd say, "Oh, wait, wait, I overshot 473." So a hundred is too high. So then you would back up a little bit. And then you could say, "All right, I'm gonna go for low numbers "and just slowly chip away at it." So you might say that five goes into 473. You know it goes more than 20 times. Let's just start with 20. Well, what is 20 times five? 20 times five is 100. And let me be very clear what that is. That is 20 times our five right over there. And so clearly we did not overshoot it, but how many more times can five go into 473 than 20? To figure that out, we figure out how much more we have left over to go, so we subtract the hundred from 473. And we have 373. So how many times can five go into 373? Well, if 20 times five was a hundred, well, gee, this is 300 here. So maybe we can go another 60 times. So let me put a 60 right over there. And so what is 60 times five? Well, six 10s times five would be 30 10s, which is 300. And so how much further do we have to go? So we still have 73 left. 373 minus 300 is 73. So how many times does five go into 73? Well, let's see. I know five times 12 is 60, so let me try a 12. So I'll put a 12 over here. And so 12 times five is 60, so how much further do we have to go? Let's see, 73 minus 60 is 13. And five can go into 13, so we can get a few more fives in there. Just to be clear what we're doing, we've already said, hey, we can go 20 times and then another 60 and then another 12 times. And if we go into 473 all of those times, we still have 13 left over. So we could go into, we can even fit a few more fives in there. Now, how many times does five go into 13? Well, five times two is 10. Five times three would be too much. So we could say two times. So that gets us two times five is 10. And so there what we have left over is a three. And then we can't fit any more fives in. We can't divide five into three, so that's going to give us our remainder. So how many times does five go into 473? Well, we were able to get it in there 20 times and then another 60 times and then another 12 times and then another two times. So what we can do is we can add all of these together, and what do we get? Two times plus 12 is 14, plus 60 is 74, plus 20 is 94. And then we have a remainder of three. So this is equal to 94, and then I'll write this in red, with a remainder of three. Did I do that right? Two plus 14, let's see. Two plus 12 is 14. 74, yeah, 94. Now let me just show you that there's more than one way to do this. I'll draw a little line here so we don't get it too confused. We could have done something like this. We could've said what is 473 divided by five? And we might've immediately recognized that, all right, five goes into 40 eight times. So five would go into 400 80 times at least, probably more times than that, but let's just start with 80. And so how close does that get us to 473? Well, to figure that out, we multiply 80 times five to get 400. And so can we fit any more fives into the difference? So let's figure out the difference. So we will subtract. And just to be very clear, this was 80 times five. The reason why we did that, you see how close did we get to 473? And now we wanna figure out how much do we have left over? How many more fives can we fit in? And so you subtract 400 from 473, and we are going to get 73. Well, we can for sure fit more fives into 73. We might say, hey, maybe let's try to fit another 10 fives in there. So let's stick another 10 fives in there. Now how close are we? Well, 10 times five is 50. And to be clear, what we just did here is we multiplied 10 times five. And now can we fit any more fives in? Well, to figure that out, we would need to subtract and figure out what we have left. So 73 minus 50, that's going to be 23. And we can for sure fit more fives into 23. We know that five times four is equal to 20. So let's put four more fives in there. So four times five is going to be 20. Let's see how close we are now. And to be very clear, that is four times our five. And so what do we get to? What do we have left? Can we fit any more fives in? Let's see, 23 minus 20 is just three. And that's less than five, so we can't fit any more fives in, so there we have it. We were able to get 80 fives into 473. We saw that we still had some left over. We were able to fit another 10 into that leftover. And then we still saw that we had some left over. We were able to fit another four into that leftover. And then we had a leftover of three and we weren't able to fit any more fives in. And so in total, we were able to fit 94 fives into 473, and then we had three left over, which is exactly what we had there.